') + ')', 'gi'); if (regex.test(text)) { found = true; var frag = document.createDocumentFragment(); var parts = text.split(regex); parts.forEach(function(part, i) { if (i % 2 === 0) { frag.appendChild(document.createTextNode(part)); } else { var span = document.createElement('span'); span.className = 'userscript-highlight'; span.textContent = part; frag.appendChild(span); } }); node.parentNode.replaceChild(frag, node); } }); } else if (node.nodeType === 1 && node.childNodes) { // element var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT']; if (!skipTags.includes(node.tagName)) { Array.from(node.childNodes).forEach(highlight); } } } highlight(document.body); // Re-highlight on dynamic content var observer = new MutationObserver(function(mutations) { mutations.forEach(function(m) { m.addedNodes.forEach(function(node) { if (node.nodeType === 1 || node.nodeType === 3) highlight(node); }); }); }); observer.observe(document.body, { childList: true, subtree: true }); })(); } } catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + ', 'i'); if (__m === '*' || __re.test(location.href)) { // Strip utm_, fbclid, gclid, etc. from all links on page (function() { var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content', 'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid', 'ref', 'ref_src', 'source', 'medium', 'campaign']; function cleanUrl(url) { try { var u = new URL(url, window.location.origin); var changed = false; trackingParams.forEach(function(p) { if (u.searchParams.has(p)) { u.searchParams.delete(p); changed = true; } }); return changed ? u.toString() : url; } catch (e) { return url; } } function cleanLinks() { document.querySelectorAll('a[href]').forEach(function(a) { var clean = cleanUrl(a.href); if (clean !== a.href) a.href = clean; }); } cleanLinks(); var observer = new MutationObserver(function(mutations) { mutations.forEach(function(m) { m.addedNodes.forEach(function(node) { if (node.nodeType === 1) { if (node.tagName === 'A') cleanLinks(); node.querySelectorAll('a[href]').forEach(function(a) { var clean = cleanUrl(a.href); if (clean !== a.href) a.href = clean; }); } }); }); }); observer.observe(document.body, { childList: true, subtree: true }); })(); } } catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); } })(); (function(){ try { var __m = "youtube.com"; var __re = new RegExp('^' + "youtube\\.com" + ', 'i'); if (__m === '*' || __re.test(location.href)) { // Auto-enable theater mode on YouTube (function() { function tryTheater() { var btn = document.querySelector('button[aria-label="Theater mode"], ytd-player #player button[title="Theater mode"]'); if (btn && !btn.classList.contains('activated')) { btn.click(); } } // Try immediately tryTheater(); // Try after navigation (SPA) var lastUrl = location.href; setInterval(function() { if (location.href !== lastUrl) { lastUrl = location.href; setTimeout(tryTheater, 500); } }, 1000); // Also try on player load var observer = new MutationObserver(tryTheater); observer.observe(document.body, { childList: true, subtree: true }); })(); } } catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); } })(); (function(){ try { var __m = "*"; var __re = new RegExp('^' + ".*" + ', 'i'); if (__m === '*' || __re.test(location.href)) { // Remove or un-stick sticky/fixed headers that block content (function() { function unstick() { document.querySelectorAll('header, nav, [role="banner"], .header, .navbar, .sticky, .fixed-top, [style*="position: fixed"], [style*="position:sticky"]').forEach(function(el) { if (el.style.position === 'fixed' || el.style.position === 'sticky' || getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') { el.style.position = 'static'; el.style.top = 'auto'; el.style.zIndex = 'auto'; } }); } unstick(); var observer = new MutationObserver(unstick); observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] }); })(); } } catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); } })(); })(); Add P219 Toronto by StevenClontz · Pull Request #1395 · pi-base/data · GitHub
Skip to content

Add P219 Toronto - #1395

Closed
StevenClontz wants to merge 6 commits into
mainfrom
StevenClontz/20250813/toronto
Closed

Add P219 Toronto#1395
StevenClontz wants to merge 6 commits into
mainfrom
StevenClontz/20250813/toronto

Conversation

@StevenClontz

@StevenClontzStevenClontz commented Aug 14, 2025

Copy link
Copy Markdown
Member

No description provided.

@Moniker1998

Moniker1998 commented Aug 17, 2025

Copy link
Copy Markdown
Collaborator

@StevenClontz is this a meme draft?

@StevenClontz

StevenClontz commented Aug 17, 2025

Copy link
Copy Markdown
MemberAuthor

Admittedly, @ccaruvana@lyengulalp@jocelynbell and others did put this together with me at the SumTopo banquet dinner, as a bit.

It can be ignored for now, but I think it would make a legitimate contribution after some polish. It is discussed in e.g. Open Problems in Topology pg 15. Whether we include the "rules" for discussing the Toronto problem is up for debate I suppose. (They don't belong as meta-properties of course.)

@prabau

prabau commented Aug 17, 2025•
edited
Loading

Copy link
Copy Markdown
Collaborator

Yeah, I was wondering if this was a "joke" property.

But, has this notion received enough attention with some interesting results/spaces to be worth including in pi-base?

@StevenClontz

StevenClontz commented Aug 17, 2025

Copy link
Copy Markdown
MemberAuthor

The latest commit provides the motivation: it's open whether in ZFC there exist uncountable non-discrete Toronto spaces.

@prabau

prabau commented Aug 17, 2025

Copy link
Copy Markdown
Collaborator

https://mathoverflow.net/questions/24144/is-there-an-uncountable-non-discrete-hausdorff-toronto-space

https://en.wikipedia.org/wiki/Toronto_space

@StevenClontz

StevenClontz commented Aug 17, 2025

Copy link
Copy Markdown
MemberAuthor

So this search would be the Toronto problem: https://topology.pi-base.org/spaces?q=%7ECountable%2B%7EDiscrete%2BHausdorff%2BToronto (I forgot Hausdorff earlier)

To make this a serious PR, I need to add relevant facts about Toronto: it's implied by discrete and indiscrete, it's satsified by co-finite topologies, etc.

@prabau

prabau commented Aug 17, 2025

Copy link
Copy Markdown
Collaborator

From the mo post above: "Under GCH the only Hausdorff Toronto spaces (of any cardinality) are the discrete spaces."

So there won't be any non-discrete Hausdorff example in ZFC.

@prabau

prabau commented Aug 17, 2025•
edited
Loading

Copy link
Copy Markdown
Collaborator

Lots of great stuff in W. Brian, "The Toronto problem" https://zbmath.org/1286.54032

@Moniker1998Moniker1998 changed the title Add P217 TorontoAdd P219 TorontoAug 29, 2025
@Moniker1998

Moniker1998 commented Dec 16, 2025

Copy link
Copy Markdown
Collaborator

@StevenClontz are you going to work on this PR?

@felixperneggerfelixpernegger mentioned this pull request Dec 24, 2025
Closed
@Moniker1998

Moniker1998 commented Dec 27, 2025

Copy link
Copy Markdown
Collaborator

@prabau should we close this PR?

@prabau

prabau commented Dec 27, 2025

Copy link
Copy Markdown
Collaborator

Yes, it seems so. @StevenClontz this work is being subsumed by #1549. So to keep things tidy, it seems we can close this PR and do any additional work in #1549.

Note that there are some valuable comments and references in the current PR and #1549 should make sure anything useful here is made use of.

@prabauprabau closed this Dec 27, 2025
@StevenClontz

StevenClontz commented Jan 14, 2026

Copy link
Copy Markdown
MemberAuthor

Thanks for not letting me hold this up. 👍

Sign up for freeto join this conversation on GitHub. Already have an account? Sign in to comment

Reviewers

@ccaruvanaccaruvanaAwaiting requested review from ccaruvana

Assignees

No one assigned

Labels

property

Projects

None yet

Milestone

No milestone

Development

Successfully merging this pull request may close these issues.

3 participants

@StevenClontz@Moniker1998@prabau