Talk:Topology

Cows, like all vertebrates, have a passage going right through them from the mouth to the anus. Contrary to the rather good animation in the article, cows are therefore doughnuts, not spheres. SpinningSpark 14:52, 21 February 2019 (UTC)

Sure, but the cow's mouth is closed, and let's say its anus is rather...erm...clenched, so it's in fact hollow, and therefore at least homotopy equivalent to a sphere, if not actually homeomorphic. It's the nostrils you have to worry about. But seriously, as just a gentle hand-wavy depiction of things, it's probably okay, especially given that it's likely a nod to the spherical cow joke. Maybe just a footnote in the caption or something would suffice to clarify. –Deacon Vorbis (carbon • videos) 15:11, 21 February 2019 (UTC)

I tend to agree somewhat with both arguments: the cow-into-sphere homeomorphism is not perfect. In fact, mammals have many orifices, pores, etc. I think the mug-into-doughnut homeomorphism is appropriate and arguably a classic, but I think the cow-into-sphere homeomorphism should be removed from this article.—Anita5192 (talk) 17:44, 21 February 2019 (UTC)

A cow is a donut, the contents of the gut are topologically outside of the animal. The nostrils are the openings to an invagination, they are equivalent to the part of the cup that holds the liquid. (Although the nostrils can be thought of as a hole because you can go in one and out the other. However, it is more biologically accurate to think of them as two invaginations that joined on the inside, because that is what happened in evolutionary history.) The urogenital system, sweat glands and ear holes are also invaginations. So the bladder, urethra and ureter are topologically on the outside. This has biological significance because anything that is topologically outside of the body has a microbiome. 2001:56A:F9D6:3900:1CA7:D297:11F:FFA6 (talk) 07:56, 27 October 2025 (UTC)

I came to this article from AN/I and am almost entirely ignorant of the topic. An IP editor was changing this quotation: ""the study of qualitative properties of certain objects (called topological spaces) that are invariant under a certain kind of transformation (called a continuous map), especially those properties that are invariant under a certain kind of invertible transformation (called homeomorphisms)" to a summary in their own words. I cannot find the source of that quote (I found only a blog post that I suspect copied from this article), and it is not stated in the article. That means it can't stay, as it is not attributed to the source. Given my ignorance, I'm going to temporarily revert to the IP's paraphrase and insert a hidden comment. I'll then try WikiBlame in case there was attribution in the history. Pinging Blackmane and Sasquatch, who posted in the now closed AN/I section. Yngvadottir (talk) 19:18, 25 June 2019 (UTC)

The Wikiblame tool is down, but I believe the quote was first introduced without attribution by Anilkumarphysics in this 2009 edit. Unless some of their contributions have been deleted, rewriting this article appears to have been all they did. So there may be other unattributed material they introduced elsewhere in the article. Now pinging Deacon Vorbis and Anita5192, the two editors who reverted the IP, to consider the IP's version on the merits (unless someone can find the source of the quote so we can just attribute it). Yngvadottir (talk) 19:33, 25 June 2019 (UTC)

You can go ahead and edit it as you wish. There are no content issues with that IP. The blocked IP generally makes good contributions but is likely linked to WP:LTA/BKFIP, a problematic user who is community banned. Sasquatch t|c 19:42, 25 June 2019 (UTC)

I know BKFIP quite well. But regardless of whether this was them, I am not qualified to edit mathematics articles. (And since the IP edit warred, my partial restoration of their version was impolite to the other editors involved.) Yngvadottir (talk) 19:47, 25 June 2019 (UTC)

Ah, cool cool. That is very polite of you. :-) Sasquatch t|c 20:03, 25 June 2019 (UTC)

IMO, both versions are equally bad. The IP's version is slightly worse as wrongly asserting that topology is the study of some topological spaces, not of all of them (restrictive "that" in the first sentence). Moreover this section "Introduction" is aimed to duplicate the lead, which is much better. So, this section deserves for a major edit. In such a case, Wikipedia rule is to keep the stablest version until a consensus is reached on the talk page (here). So, I'll restore the older version. D.Lazard (talk) 20:05, 25 June 2019 (UTC)

But the older version contains an unattributed quote, which is plagiarism! Yngvadottir (talk) 20:11, 25 June 2019 (UTC)

The use of quotes does not means necessarily that this is a quotation. Many editors use quotes for emphasis, and this seems the case here. I have thus removed the quotation marks. If this were a quotation, the poor formulation suggests that its author is not notable enough for being quoted in Wikipedia. So, unless someone can provide evidence of a copyvio, the sentence must be credited to the editor that introduced it. D.Lazard (talk) 21:08, 25 June 2019 (UTC)

Umm, no, that would violate the rights of the writer if it is, indeed, a quotation. And I've never encountered such a usage, quotation marks for emphasis. Are you perhaps confusing quotation marks with the use of double single quote marks/apostrophes to make italics in wiki-markup? If you do know of any uses of actual quote marks for other than quotations in articles, they need to be removed ASAP. In the meantime, I really hope someone else will fix that paragraph to eliminate the possibility of plagiarism along with the unclarity. Yngvadottir (talk) 21:41, 25 June 2019 (UTC)

Sorry, "emphasis" is not the right word. Quotation marks are often used for parts of speech that are considered for themselves, and this is not discouraged by WP:MOS#Words as words, were an example is given that is not a quotation. Specifically in mathematics, definitions and statements are often considered this way and surrounded by quotation marks when included in a larger sentence, as it is the case here. My personal opinion is that this is not a good practice, and that this must be avoided, generally by putting the definition or statement in its own sentence. Here, this is definitely not useful to quote the provided definition or to split the sentence; therefore, I have removed the quotation marks. D.Lazard (talk) 08:48, 26 June 2019 (UTC)

(edit conflict) @Yngvadottir: Sorry for the delay, and I appreciate the heads-up. Definitely no worries from you about whatever you've done. As for the statement itself, both versions have problems, but I'm honestly feeling really burned out right now, and I need a bit of a break. If I get some energy for it and remember, I'll try to take another look. –Deacon Vorbis (carbon • videos) 21:47, 25 June 2019 (UTC)

I'm not much more qualified to edit maths articles than @Yngvadottir:. My response to the IP was more in line with what is accepted practice and less about the actual content itself. I did notice that the quote wasn't attributed. In fact a lot of text following it wasn't sourced, and was intending to have a longer read to see if there was a source further down that was being used, but got side tracked by Real Life™. Blackmane (talk) 23:34, 25 June 2019 (UTC)

Then I'll park this info here for discussion. This is the sum of the changes by Anilkumarphysics: consecutive edits at the top of the Introduction section (then headed Elementary introduction), all but the last three adding text. The section previously began with "Topological spaces show up naturally in almost every branch of mathematics. This has made topology one of the great unifying ideas of mathematics." - that and what follows appear to a cursory glance to have remained unchanged. If what's intended is indeed an elementary introduction to the field, dare I suggest the best solution is to revert Anilkumarphysics and go back to starting with what looks like a simple overview? Maybe some of the links could or should be reinserted elsewhere. I cannot emphasise too much how little I know about mathematics. Yngvadottir (talk) 23:46, 25 June 2019 (UTC)

I agree to simply removing the two paragraphs added by the WP:SPA: they do not add anything relevant to this section, and make the object of the section confusing. The third paragraph is also to be removed because its WP:PEACOCK style ("great unifying ideas of mathematics"). Without these three paragraphs, the section becomes a rather good explanation of the purpose of topology. However the heading is confusing (and I have been confused by it, see above). "Motivation" would be clearer. Moreover, these explanations would better placed before section "History", as they are useful for understanding this section. I'll be bold and do these modifications.

By the way, the lead has also several issues, but fixing them is another task. D.Lazard (talk) 09:30, 26 June 2019 (UTC)

Thank you, that seems clearer to me. Yngvadottir (talk) 21:30, 27 June 2019 (UTC)

the intro is one of the best math intros I have read; one of the very very few pitched at the right level, without to much jargon congrats — Preceding unsigned comment added by 2601:192:4701:BE80:6CCC:C42E:B519:9520 (talk) 03:11, 19 February 2020 (UTC)

I agree, but this page is meant for improving the article. The fact that no algebra or calculus is needed is possibly responsible for the fact that the article is easy to understand.

A discussion is taking place to address the redirect Tapology. The discussion will occur at Wikipedia:Redirects for discussion/Log/2020 September 1#Tapology until a consensus is reached, and readers of this page are welcome to contribute to the discussion. 1234qwer1234qwer4 (talk) 18:18, 1 September 2020 (UTC)

The introduction gives the reader who is unfamiliar with topology the impression that topology is just about squishing and bending shapes. Yes, we can use topology to describe how we can deform surfaces but this is just one side of the very diverse field and I find this overgeneralisation kind of hideous and cruel to those who are interested in studying topology. I know that I myself was under the impression that "topology is when holes and funny shapes" when I first read this article and knew nothing about it so that is how I know that this sort of water-downed explanation does not benefit anybody.

I think it would better to introduce topology as a way to generalise/formalise concepts like open and closed-ness, connectedness, continuity etc and talk about its usefulness in areas like analysis. Then we can move on to the part about continuous deformation. I'm not saying it is necessary to be super formal and technical but we should not sacrifice accuracy to make the reader feel like they understand it when they don't. Raccoon bestie (talk) 11:19, 23 July 2022 (UTC)

@Raccoon bestie: that's certainly a reasonable idea. WP:LEDE says the intro is supposed to introduce the topic and summarize or at least identify the main ideas of the article. Wanna take a shot at writing what you are envisioning? It sounds like you're proposing a major overhaul of the intro, not just a little word-smithing, so maybe it's a good idea to hash it out here on the talkpage rather than on the live article. DMacks (talk) 15:12, 23 July 2022 (UTC)

I agree with this as these appear to be the topics in an introductory book of topology. The intro should at least be rewritten to say there's a bit more to it than bending shapes. MartensCedric (talk) 19:18, 28 December 2023 (UTC)

... crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. I think these terms need to be refined before the opening paragraph is made sufficiently rigorous. — Preceding unsigned comment added by 108.41.98.105 (talk) 20:16, 27 May 2023 (UTC)

I might have expected it, no? Not that I'm a mathematician. --MilkMiruku (talk) 01:42, 1 August 2023 (UTC)

The second paragraph of the lead includes the misleading text compactness, which allows distinguishing between a line and a circle;. I suggest compactness, which allows distinguishing between a line and a closed segment;.

I'd like to see a mention of the circle not being a contractible space, or having a trivial fundamental group, but that's definitely too technical for the lead and perhaps for the article. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 18:38, 4 June 2025 (UTC)

A recent series of edits and reverts raises a question. While the subject of the edits appears to be a crank, I know that there are a lot of significant Moslems in the sciences, and I would be astounded if there were none in Topology. I know for a fact that there are prominent Asian Topologists.

The article doe not seem to be explicitly Euro-centric, but I believe that it would be improved by mention of modern contributions from other continents. -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 14:35, 7 August 2025 (UTC)

There no Spanish, no English, no Russian mathematicians cited in the article (although Arnold deserves probably to be cited), If you know any topologist, Muslim of not, that have conributions important enough to be cited in a 20-lines history, feel free to add them to the article. There are great Muslim mathematicians, but all those that I know lived centuries before the introduction of topology. D.Lazard (talk) 17:41, 7 August 2025 (UTC)

I know that Italy was major in algebraic geometry. What about topology? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 18:10, 7 August 2025 (UTC)

Betti for sure. Maybe Peano? Tito Omburo (talk) 18:13, 7 August 2025 (UTC)

FWIW, I think Sullivan's Abel prize is undue weight. Modern topology is huge and rarefied. If we're going to mention non-European contributions, they mostly postdate the foundations of the subject. E.g., Banyaga, Fukaya, maybe Toda. But I think we just keep this to foundations, which happened in Europe. That having been said, we absolutely should mention more Russians (Alexandrov, Urysohn, Pontryagin.) Maybe some Poles too (e.g., Sierpiński, maybe Kuratowski.) Tito Omburo (talk) 17:57, 7 August 2025 (UTC)

Do people in, e.g., characteristic classes, fiber bundles, homotopy theory, belong in the article, or are they too specialized? -- Shmuel (Seymour J.) Metz Username:Chatul (talk) 18:47, 7 August 2025 (UTC)

I would think such people would have a place in a history of topology (currently a redirect here) article. The history here is pretty anemic overall. James's History of Topology provides a collection of articles. The table of contents is suggestive as to possible milestones. Tito Omburo (talk) 19:45, 7 August 2025 (UTC)

The current versions says:

Two-dimensional manifolds are also called surfaces, although not all surfaces are manifolds. Examples include the plane, the sphere, and the torus, which can all be realized without self-intersection in three dimensions, and the Klein bottle and real projective plane, which cannot (that is, all their realizations in three dimensions are surfaces that are not manifolds).

This can be read as stating that the Klein bottle and the real projective plane are not manifolds. I think we could be more precise about this - sure, the embeddings of those manifolds in R3 are not manifolds, but the spaces themselves are i.e. the non-manifoldness is an artifact of the embedding, not a property of the space itself.

I'll try to come up with some better language. Mr. Swordfish (talk) 02:48, 29 October 2025 (UTC)

As I see it, in topology a surface is a 2-D manifold. In algebraic geometry, a surface may not be a manifold because of self-intersection.

I don't think we need to go into the details of topology vs algebraic geometry nomenclature in the article about topology, so I'm going to remove the extraneous detail that some surfaces are not manifolds. Mr. Swordfish (talk) 13:40, 29 October 2025 (UTC)