Talk:Surface (topology)

message: Please rewrite the entire article, and put the existing content into other articles that go into the technical and esoteric details of surface. Here is what I mean.
The current draft of the article is too esoteric and too technical. It should be rewritten for the general audience and have references to other articles that go into more technical and esoteric detail. It does not provide a starting place for learning about surfaces. The general reader is a high school and university freshman who needs to quickly learn about surfaces and learn where they can get more information if they need it.
The article does not clearly and simply tell the reader what is a surface, and what are the different classes or types of surfaces. For example, what is a closed surface and what is an open surface.
An introduction should start from a short historical point of view, and remain conscience of the reader whose purpose is to learn about surfaces, and learn where they can get more information or details about subtopics to surfaces. No esoteric jargon should be used in simple discussions about an introduction to surfaces, and only limited and defined technical jargon should be included.
--Thomas Foxcroft, July 16, 2009  —Preceding unsigned comment added by Thomas Foxcroft (talk • contribs) 01:13, 17 July 2009 (UTC)
thread_title:  Opinion From a Reader 

message: Suggestions:
* Better graphics under "Some models", and add a higher genus example such as genus 2. 
* A discussion of constant curvature metrics on surfaces, connections with the Gauss-Bonnet theorem and the Uniformization Theorem.
--Mosher 14:41, 21 September 2005 (UTC)
thread_title: Two suggestions

message: The treatment of fundamental polygons here (and on the page dedicated to the subject) seems meaningless.
For example, there is no definition of the mechanism where attaching sides with labels yields the indicated surface.
:On a non-rigorous level, imagine that the polygons are rubber sheets. Sew or glue the matching sides together. At least in a couple of cases (torus, sphere) it is easy to convince yourself that you get the claimed surface. A rigorous proof would not be useful for Wikipedia, I think.
Is this a purely arbitrary notation?  Or is there some reason for its use?
:The choice of symbols (A, B, etc.) for the sides is arbitrary. All that matters is that we know which sides to match with which (i.e. A with A), and which direction to match them in (i.e. so that the arrows point in the same direction).
(The page dedicated to fundamental polygons seems to indicate that this notation has something to do with group isomorphisms, but without any examples or other basic orientation the discussion seems inaccessible to someone like me without a background in the topic.)
159.54.131.7 14:26, 2 October 2007 (UTC)
replies: text: To understand this part of the article, you need to understand groups, group presentations, the fundamental group, and the Seifert-van Kampen theorem. This article cannot explain all of these points, but it does at least mention all of them. I think the detail you want should be provided by the fundamental polygon article, not this article. Joshua R. Davis 16:16, 2 October 2007 (UTC)
thread_title:  Fundamental polygons? 

message: This aspect of the geometry of surfaces and its tie-up with Euler characteristic seems to be entirely missing from the article at the moment. This classical material can be found in standard textbooks, such as those of Barrett O'Neill and Singer & Thorpe. --Mathsci 20:24, 6 November 2007 (UTC)
replies: text: Agreed; this is a serious omission at present. By the way, good work on your recent edits. Joshua R. Davis 23:10, 6 November 2007 (UTC)
thread_title: Gauss-Bonnet theorem and curvature

message: Over the past three days there have been about 60 edits to this article from just two editors. They're good edits, but very close in time -- sometimes within a minute of each other. Surely this is an opportunity for the preview button? Joshua R. Davis 16:36, 14 November 2007 (UTC)
replies: text: The preview button is being used, but this is not so easy to write. At the moment I am working out how to put the Alexandrov inequality in completely elementary terms. I also had to write all the maths of the article on the Cauchy-Kowalevski theorem. M.H. is the consultant beautician for the added section. Please be patient: major additions are bound to require a lot of edits and reordering/corrections as the content evolves. --Mathsci 17:05, 14 November 2007 (UTC)
thread_title:  Previewing 

message: I think that the first paragraph contains quite an innacurate sentence:
"On the other hand, there are surfaces which cannot be embedded  in three-dimensional Euclidean space without introducing singularities or intersecting itself — these are the unorientable surfaces."
I do not agree. What about a Mobius band, considered as an open surface, or possibly as a surface with boundary?. It certainly isn't orientable and certainly can be embedded into three-dimensional Euclidean space, as you should be able to convince yourself by constructing one yourself in what we conceive as 3-dimensional space...  —Preceding unsigned comment added by Jjw19 (talk • contribs) 20:21, 25 March 2010 (UTC)
replies: text: [I moved your comment to the end of the page.] You are certainly correct. I'll fix it. In the future, feel free to fix such things yourself. Mgnbar (talk) 18:35, 8 April 2010 (UTC)
thread_title:  Orientability 

message: I'd like to merge the closed surface stub and the section here on the classification theorem. Should there be a separate article for closed surfaces or should closed surfaces link to here? Richard Thomas (talk) 04:28, 19 July 2010 (UTC)
replies: text: I agree with you; that stub should be merged into this article. Mgnbar (talk) 12:43, 19 July 2010 (UTC)
thread_title:  Merging closed surface 

message: The article seems to switch arbitrarily between En and Rn to describe Euclidean n-space.  It would be less confusing to stick with one; I have never seen En used, and suggest sticking with the standard Rn.  HawaiianEarring (talk) 14:24, 12 April 2011 (UTC)
thread_title:  Reader Suggestion about difference between ''E<sup>n</sup>'' and ''R<sup>n</sup>'' 

message: Maybe this article should be called "Real surface", and "real dimension two" should be put in the first line?  — Preceding unsigned comment added by 78.239.179.184 (talk) 19:40, 8 November 2011 (UTC)
replies: text: Real surfaces are by far the most common kind of mathematical surfaces that readers are going to seek. On the other hand, it could be argued that mathematics doesn't own the concept of surface at all. For example, there's surface science and even surface art. My long-term hope is that Surface will be a disambiguation page. When that happens, maybe "Real surface" will be the ideal title for this article. Mgnbar (talk) 00:17, 9 November 2011 (UTC)
thread_title:  Name 

message: I think this article's title may be misleading to some Wikipedia editors, since many links to surface may not be about surfaces in the context of topology. I think this article should be renamed so that Surface will redirect to Surface (disambiguation), since many articles about other types of surfaces would otherwise link to this page misleadingly. Jarble (talk) 15:25, 22 March 2013 (UTC)
thread_title: Should this article be renamed to ''Surface (topology)'', for the purpose of disambiguation?

message: I think this example confuses rather than explains the notion of local compactness.
"For example, the surface of the Earth is (ideally) a two-dimensional sphere, and latitude and longitude provide two-dimensional coordinates on it (except at the poles and along the 180th meridian)."
:It's not about local compactness. It's about how the surface of the Earth is a two-dimensional manifold, rather than a three-dimensional one, as many non-mathematical readers might guess.
:The sentence would read more smoothly without the parenthetical disclaimers. But they are important to keeping the sentence correct. You are welcome to propose a re-wording here on the talk page. Mgnbar (talk) 14:45, 15 October 2015 (UTC)
thread_title:  Redundant intro sentence 

message: Thinking again about the discussion of the previous section, it appears that the title of the article must correspond to a Broad-concept article, and that the body is restricted to Topology of surfaces (similarly we have Differential geometry of surfaces). We have thus to rename the article, and to write the broad-concept article. This article, renamed Surface (topology), will be sub-articles of the broad-concept one, as well as Surface (differential geometry) and Surface (algebraic geometry) (these are redirects that I have just created for harmonizing titles and making research easier). 
From this point of view, the new lead is not adapted to the body. It is also not convenient for the broad concept article. A witness of this is that the most popular example of surface is the graph of a bivariate continuous function, and that this example is not cited in the article, although it is fundamentally the basis of the concept of a two-dimensional manifold. 
Therefore, I'll move Surface to Surface (topology) (through a move request), and start to write the broad-concept article, which will be a stub at the beginning. D.Lazard (talk) 09:41, 6 April 2016 (UTC)
thread_title:  Lacking broad-concept article 

message: Hello fellow Wikipedians,
I have just modified one external link on Surface (topology). Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive https://web.archive.org/web/20100612090500/http://new.math.uiuc.edu/zipproof/zipproof.pdf to http://new.math.uiuc.edu/zipproof/zipproof.pdf
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
Cheers.—InternetArchiveBot (Report bug) 05:53, 2 December 2017 (UTC)
thread_title:  External links modified 

message: In the article it is stated that
'the existence of the Prüfer surface shows that there exist two-dimensional complex manifolds (which are necessarily 4-dimensional real manifolds) with no countable base. (This is because any n-real-dimensional real-analytic manifold Q can be extended to an n-complex-dimensional complex manifold W that contains Q as a real-analytic submanifold.)'
The statement in parentheses is false. The Long Line carries a real analytic structure but it is not a submanifold of a complex-1-dimensional manifold because that would have to be a nonmetrizable Riemann surface which does not exist by Rado's theorem.
The reason that there is complex-2-dimensional analog of the Prüfer manifold is that it is clear from the construction that you can construct the Prüfer manifold and replace all real numbers by complec numbers.
Am I right or am I missing something?
--2A00:1398:200:202:6146:6249:BF2B:816 (talk) 09:29, 10 September 2018 (UTC)
thread_title:  complexification of non-metrizable manifoldd 

message: I see a section about surfaces with boundary (6.3) within a section about closed surfaces (6). This suggests the sections need rearranging. Karl (talk) 12:42, 26 May 2021 (UTC)
replies: text: Good point. I did a bunch of reorganizing. There is still a lot of polishing to do. Mgnbar (talk) 17:39, 26 May 2021 (UTC)
thread_title:  Closed Surfaces and Surfaces with Boundary 

message: I have reverted in this article and in Surface (mathematics) a sentence mentioning hypersurfaces as examples of manifolds, together with curves and surfaces. This is wrong as many hypersurfaces are not manifolds. Moreover, even if it were mathematically correct, the sentence would be confusing, as the reason of adding the sentence (linking to Hypersurface) is hidden in a sequence of examples of a topic that is not the subject of the article.
I have added a link to Hypersurface in  D.Lazard (talk) 07:57, 28 September 2021 (UTC)
thread_title:  Why does hypersurface not belong on either this page, or the other "surface" page? 

message: Fgnievinski, I understand the point of your edit now. The wording is more confusing than it needs to be. How about: "A surface embedded in three-dimensional space is closed if and only if it is the boundary of a solid?" Mgnbar (talk) 02:02, 10 November 2021 (UTC)
thread_title:  Closed surfaces enclosing volume 

message: The redirect 2-space has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.  fgnievinski (talk) 04:51, 7 December 2023 (UTC)
thread_title:  "[[:2-space]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]]