Completing S56 and S206 (deleted sequence topology)

[pzjp]

Several missing traits, zbMath references, cleanup

Note that locally metrizable will be resolved by "locally orderable metrization theorem".

P120 has to be added in a future PR.

[yhx-12243]

Remark: S56 is very similar to S206 (the only difference is semiregularity), you can complete them together if you like.

[pzjp]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

[yhx-12243]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

Yes they're almost the same. However adding new space should be postpone to new issues/PRs.

I only suggests you can almost copy your update to S206, if possible, and I think the review wouldn't take more time.

[pzjp]

I know it comes from the original post, but taking intervals $[\frac1{2n+1},\frac1{2n}]$ (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

[yhx-12243]

I know it comes from the original post, but taking intervals [ 1 2 n + 1 , 1 2 n ] (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

Maybe it can be added to the description, depends on other's mind (I don't mind).

Also, S206|P56 can be cleaned up, similar to S56.

[prabau]

I have absolutely no problem in changing the definition of S206 as suggested. I agree it's a little better.

As for this PR, this already has 17 changed files, so it's probably enough to review and merge. S206 can be done afterwards and it's indeed mostly parallel. Further changes to S56 could be done at the same time if needed.

[pzjp]

I realised that fixed point for the circular version would be tricky (may hold; similar to the Warsaw circle).

[yhx-12243]

Are there more progress about this?

[pzjp]

Actually David Gao has changed $3^n$ in StackExchange post according to my suggestion. I guess we should incorporate it to $\pi$-Base now.

[pzjp]

The lack of local connectedness (P41) for S206 will follow from locally orderable (P120; not available in this branch) and T754.

[prabau]

I reviewed everything and it all looks good.

But since we need T756, marking this as Draft until #1393 is merged.

[prabau]

Sorry, it seems I was confused. We don't need T756 for this. So approving and merging now.

[pzjp]

Several missing traits, zbMath references, cleanup

Note that locally metrizable will be resolved by "locally orderable metrization theorem".

P120 has to be added in a future PR.

[yhx-12243]

Remark: S56 is very similar to S206 (the only difference is semiregularity), you can complete them together if you like.

[pzjp]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

[yhx-12243]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

Yes they're almost the same. However adding new space should be postpone to new issues/PRs.

I only suggests you can almost copy your update to S206, if possible, and I think the review wouldn't take more time.

[pzjp]

I know it comes from the original post, but taking intervals $[\frac1{2n+1},\frac1{2n}]$ (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

[yhx-12243]

I know it comes from the original post, but taking intervals [ 1 2 n + 1 , 1 2 n ] (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

Maybe it can be added to the description, depends on other's mind (I don't mind).

Also, S206|P56 can be cleaned up, similar to S56.

[prabau]

I have absolutely no problem in changing the definition of S206 as suggested. I agree it's a little better.

As for this PR, this already has 17 changed files, so it's probably enough to review and merge. S206 can be done afterwards and it's indeed mostly parallel. Further changes to S56 could be done at the same time if needed.

[pzjp]

I realised that fixed point for the circular version would be tricky (may hold; similar to the Warsaw circle).

[yhx-12243]

Are there more progress about this?

[pzjp]

Actually David Gao has changed $3^n$ in StackExchange post according to my suggestion. I guess we should incorporate it to $\pi$-Base now.

[pzjp]

The lack of local connectedness (P41) for S206 will follow from locally orderable (P120; not available in this branch) and T754.

[prabau]

I reviewed everything and it all looks good.

But since we need T756, marking this as Draft until #1393 is merged.

[prabau]

Sorry, it seems I was confused. We don't need T756 for this. So approving and merging now.

[pzjp]

Several missing traits, zbMath references, cleanup

Note that locally metrizable will be resolved by "locally orderable metrization theorem".

P120 has to be added in a future PR.

[yhx-12243]

Remark: S56 is very similar to S206 (the only difference is semiregularity), you can complete them together if you like.

[pzjp]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

[yhx-12243]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

Yes they're almost the same. However adding new space should be postpone to new issues/PRs.

I only suggests you can almost copy your update to S206, if possible, and I think the review wouldn't take more time.

[pzjp]

I know it comes from the original post, but taking intervals $[\frac1{2n+1},\frac1{2n}]$ (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

[yhx-12243]

I know it comes from the original post, but taking intervals [ 1 2 n + 1 , 1 2 n ] (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

Maybe it can be added to the description, depends on other's mind (I don't mind).

Also, S206|P56 can be cleaned up, similar to S56.

[prabau]

I have absolutely no problem in changing the definition of S206 as suggested. I agree it's a little better.

As for this PR, this already has 17 changed files, so it's probably enough to review and merge. S206 can be done afterwards and it's indeed mostly parallel. Further changes to S56 could be done at the same time if needed.

[pzjp]

I realised that fixed point for the circular version would be tricky (may hold; similar to the Warsaw circle).

[yhx-12243]

Are there more progress about this?

[pzjp]

Actually David Gao has changed $3^n$ in StackExchange post according to my suggestion. I guess we should incorporate it to $\pi$-Base now.

[pzjp]

The lack of local connectedness (P41) for S206 will follow from locally orderable (P120; not available in this branch) and T754.

[prabau]

I reviewed everything and it all looks good.

But since we need T756, marking this as Draft until #1393 is merged.

[prabau]

Sorry, it seems I was confused. We don't need T756 for this. So approving and merging now.

[pzjp]

Several missing traits, zbMath references, cleanup

Note that locally metrizable will be resolved by "locally orderable metrization theorem".

P120 has to be added in a future PR.

[yhx-12243]

Remark: S56 is very similar to S206 (the only difference is semiregularity), you can complete them together if you like.

[pzjp]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

[yhx-12243]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

Yes they're almost the same. However adding new space should be postpone to new issues/PRs.

I only suggests you can almost copy your update to S206, if possible, and I think the review wouldn't take more time.

[pzjp]

I know it comes from the original post, but taking intervals $[\frac1{2n+1},\frac1{2n}]$ (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

[yhx-12243]

I know it comes from the original post, but taking intervals [ 1 2 n + 1 , 1 2 n ] (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

Maybe it can be added to the description, depends on other's mind (I don't mind).

Also, S206|P56 can be cleaned up, similar to S56.

[prabau]

I have absolutely no problem in changing the definition of S206 as suggested. I agree it's a little better.

As for this PR, this already has 17 changed files, so it's probably enough to review and merge. S206 can be done afterwards and it's indeed mostly parallel. Further changes to S56 could be done at the same time if needed.

[pzjp]

I realised that fixed point for the circular version would be tricky (may hold; similar to the Warsaw circle).

[yhx-12243]

Are there more progress about this?

[pzjp]

Actually David Gao has changed $3^n$ in StackExchange post according to my suggestion. I guess we should incorporate it to $\pi$-Base now.

[pzjp]

The lack of local connectedness (P41) for S206 will follow from locally orderable (P120; not available in this branch) and T754.

[prabau]

I reviewed everything and it all looks good.

But since we need T756, marking this as Draft until #1393 is merged.

[prabau]

Sorry, it seems I was confused. We don't need T756 for this. So approving and merging now.

[pzjp]

Several missing traits, zbMath references, cleanup

Note that locally metrizable will be resolved by "locally orderable metrization theorem".

P120 has to be added in a future PR.

[yhx-12243]

Remark: S56 is very similar to S206 (the only difference is semiregularity), you can complete them together if you like.

[pzjp]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

[yhx-12243]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

Yes they're almost the same. However adding new space should be postpone to new issues/PRs.

I only suggests you can almost copy your update to S206, if possible, and I think the review wouldn't take more time.

[pzjp]

I know it comes from the original post, but taking intervals $[\frac1{2n+1},\frac1{2n}]$ (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

[yhx-12243]

I know it comes from the original post, but taking intervals [ 1 2 n + 1 , 1 2 n ] (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

Maybe it can be added to the description, depends on other's mind (I don't mind).

Also, S206|P56 can be cleaned up, similar to S56.

[prabau]

I have absolutely no problem in changing the definition of S206 as suggested. I agree it's a little better.

As for this PR, this already has 17 changed files, so it's probably enough to review and merge. S206 can be done afterwards and it's indeed mostly parallel. Further changes to S56 could be done at the same time if needed.

[pzjp]

I realised that fixed point for the circular version would be tricky (may hold; similar to the Warsaw circle).

[yhx-12243]

Are there more progress about this?

[pzjp]

Actually David Gao has changed $3^n$ in StackExchange post according to my suggestion. I guess we should incorporate it to $\pi$-Base now.

[pzjp]

The lack of local connectedness (P41) for S206 will follow from locally orderable (P120; not available in this branch) and T754.

[prabau]

I reviewed everything and it all looks good.

But since we need T756, marking this as Draft until #1393 is merged.

[prabau]

Sorry, it seems I was confused. We don't need T756 for this. So approving and merging now.

[pzjp]

Several missing traits, zbMath references, cleanup

Note that locally metrizable will be resolved by "locally orderable metrization theorem".

P120 has to be added in a future PR.

[yhx-12243]

Remark: S56 is very similar to S206 (the only difference is semiregularity), you can complete them together if you like.

[pzjp]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

[yhx-12243]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

Yes they're almost the same. However adding new space should be postpone to new issues/PRs.

I only suggests you can almost copy your update to S206, if possible, and I think the review wouldn't take more time.

[pzjp]

I know it comes from the original post, but taking intervals $[\frac1{2n+1},\frac1{2n}]$ (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

[yhx-12243]

I know it comes from the original post, but taking intervals [ 1 2 n + 1 , 1 2 n ] (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

Maybe it can be added to the description, depends on other's mind (I don't mind).

Also, S206|P56 can be cleaned up, similar to S56.

[prabau]

I have absolutely no problem in changing the definition of S206 as suggested. I agree it's a little better.

As for this PR, this already has 17 changed files, so it's probably enough to review and merge. S206 can be done afterwards and it's indeed mostly parallel. Further changes to S56 could be done at the same time if needed.

[pzjp]

I realised that fixed point for the circular version would be tricky (may hold; similar to the Warsaw circle).

[yhx-12243]

Are there more progress about this?

[pzjp]

Actually David Gao has changed $3^n$ in StackExchange post according to my suggestion. I guess we should incorporate it to $\pi$-Base now.

[pzjp]

The lack of local connectedness (P41) for S206 will follow from locally orderable (P120; not available in this branch) and T754.

[prabau]

I reviewed everything and it all looks good.

But since we need T756, marking this as Draft until #1393 is merged.

[prabau]

Sorry, it seems I was confused. We don't need T756 for this. So approving and merging now.

[pzjp]

Several missing traits, zbMath references, cleanup

Note that locally metrizable will be resolved by "locally orderable metrization theorem".

P120 has to be added in a future PR.

[yhx-12243]

Remark: S56 is very similar to S206 (the only difference is semiregularity), you can complete them together if you like.

[pzjp]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

[yhx-12243]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

Yes they're almost the same. However adding new space should be postpone to new issues/PRs.

I only suggests you can almost copy your update to S206, if possible, and I think the review wouldn't take more time.

[pzjp]

I know it comes from the original post, but taking intervals $[\frac1{2n+1},\frac1{2n}]$ (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

[yhx-12243]

I know it comes from the original post, but taking intervals [ 1 2 n + 1 , 1 2 n ] (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

Maybe it can be added to the description, depends on other's mind (I don't mind).

Also, S206|P56 can be cleaned up, similar to S56.

[prabau]

I have absolutely no problem in changing the definition of S206 as suggested. I agree it's a little better.

As for this PR, this already has 17 changed files, so it's probably enough to review and merge. S206 can be done afterwards and it's indeed mostly parallel. Further changes to S56 could be done at the same time if needed.

[pzjp]

I realised that fixed point for the circular version would be tricky (may hold; similar to the Warsaw circle).

[yhx-12243]

Are there more progress about this?

[pzjp]

Actually David Gao has changed $3^n$ in StackExchange post according to my suggestion. I guess we should incorporate it to $\pi$-Base now.

[pzjp]

The lack of local connectedness (P41) for S206 will follow from locally orderable (P120; not available in this branch) and T754.

[prabau]

I reviewed everything and it all looks good.

But since we need T756, marking this as Draft until #1393 is merged.

[prabau]

Sorry, it seems I was confused. We don't need T756 for this. So approving and merging now.

[pzjp]

Several missing traits, zbMath references, cleanup

Note that locally metrizable will be resolved by "locally orderable metrization theorem".

P120 has to be added in a future PR.

[yhx-12243]

Remark: S56 is very similar to S206 (the only difference is semiregularity), you can complete them together if you like.

[pzjp]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

[yhx-12243]

They are almost too similar. Wouldn't a loop-version of S206 be a more interesting example (it is e.g. path connected)?

Yes they're almost the same. However adding new space should be postpone to new issues/PRs.

I only suggests you can almost copy your update to S206, if possible, and I think the review wouldn't take more time.

[pzjp]

I know it comes from the original post, but taking intervals $[\frac1{2n+1},\frac1{2n}]$ (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

[yhx-12243]

I know it comes from the original post, but taking intervals [ 1 2 n + 1 , 1 2 n ] (instead of powers) in the definition of S206 would look a bit better and the resulting space wouldn't change.

Maybe it can be added to the description, depends on other's mind (I don't mind).

Also, S206|P56 can be cleaned up, similar to S56.

[prabau]

I have absolutely no problem in changing the definition of S206 as suggested. I agree it's a little better.

As for this PR, this already has 17 changed files, so it's probably enough to review and merge. S206 can be done afterwards and it's indeed mostly parallel. Further changes to S56 could be done at the same time if needed.

[pzjp]

I realised that fixed point for the circular version would be tricky (may hold; similar to the Warsaw circle).

[yhx-12243]

Are there more progress about this?

[pzjp]

Actually David Gao has changed $3^n$ in StackExchange post according to my suggestion. I guess we should incorporate it to $\pi$-Base now.

[pzjp]

The lack of local connectedness (P41) for S206 will follow from locally orderable (P120; not available in this branch) and T754.

[prabau]

I reviewed everything and it all looks good.

But since we need T756, marking this as Draft until #1393 is merged.

[prabau]

Sorry, it seems I was confused. We don't need T756 for this. So approving and merging now.