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GeoPhysical TopoLOGY, the movement in space[edit]

The article is severely lacking in context, topology is defined as the movement of systems (physical) in place or space, Geophysical Topology is the study of the transformation of landforms or structure throughout natural processes, applied commonly in planetary geophysics, volcanology, erosion and environmental systems, and related to any other physical transformation in any space, especially the time series modeling of processes or systems. — Preceding unsigned comment added by (talk) 06:35, 7 April 2013 (UTC)

That's topoGRAPHY, isn't it? — Arthur Rubin (talk) 08:22, 7 April 2013 (UTC)
Agreed, this is called geomorphology or perhaps changes in geophysical topography. The notion of topology is used in cartography; see for instance, Topological map and Geospatial topology. Both these links are on the Topology (disambiguation) page, so I think we have them covered.. --Mark viking (talk) 15:42, 7 April 2013 (UTC)

GA Review[edit]

This review is transcluded from Talk:Topology/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: Philroc (talk · contribs) 20:13, 10 January 2014 (UTC)

GA review (see here for what the criteria are, and here for what they are not)
  1. It is reasonably well written.
    a (prose, no copyvios, spelling and grammar): b (MoS for lead, layout, word choice, fiction, and lists):
  2. It is factually accurate and verifiable.
    a (reference section): b (citations to reliable sources): c (OR):
  3. It is broad in its coverage.
    a (major aspects): b (focused):
  4. It follows the neutral point of view policy.
    Fair representation without bias:
  5. It is stable.
    No edit wars, etc.:
  6. It is illustrated by images and other media, where possible and appropriate.
    a (images are tagged and non-free content have fair use rationales): b (appropriate use with suitable captions):
  7. Overall:

I will need a second opinion on this article because in the references section, all the references are reliable sources expect one, which is a Internet post. I don't whether to let that through or not. Philroc (talk) 17:42, 12 January 2014 (UTC)

Not to mention, since I am the recruiter I am supposed to help him out. It's all right he decided for a second opinion, I wanted to say that the lead doesn't accurately summarize the article and nor is the vice versa true. So, GA nominator, do the changes. --Ankit Maity «T § C»«Review Me» 11:34, 13 January 2014 (UTC)
Whoops! Section 2b is actually a fail because there are still "citation needed" templates scattered across the article, and the situtaion talked about previously. Thus, I am changing this articles status from second opinion status to on hold status. Philroc (talk) 11:53, 13 January 2014 (UTC)
Changed some. Address {{cn}} tags and correct the lead. Recruitee, you are requested to check out the GA review script and perform the checks accordingly. I noticed that you missed the first and most important part of MoS i.e. the lead. --Ankit Maity «T § C»«Review Me» 12:48, 13 January 2014 (UTC)
Can we please just get this over with? Philroc (talk) 11:54, 14 January 2014 (UTC)
On hold requires you to wait atleast 7 days. You put this article on hold at 11:53 13 Jan. So, mate you gotta hold till 20th. --Ankit Maity «T § C»«Review Me» 15:28, 14 January 2014 (UTC)
Can I review another article during that time? Philroc (talk) 19:33, 14 January 2014 (UTC)
Of course. But only one more. As that is a GARC process. After that, I am gonna have to show you a very detailed GA review. --Ankit Maity «T § C»«Review Me» 11:21, 15 January 2014 (UTC)
What do you mean by "After that, I am gonna have to show you a very detailed GA review"? Philroc (talk) 12:00, 15 January 2014 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── By that, I refer to the GA review that I am gonna do, so that you can see the closest details. It's a compulsory GARC step. It was supposed to be done before but sadly you went and did this review. Still, you seem to be on the right track. --Ankit Maity «T § C»«Review Me» 14:23, 15 January 2014 (UTC)

The second article I reviewed passed. Philroc (talk) 19:54, 17 January 2014 (UTC)
Nobody improved the article within the 7 days that I held the article for. Thus, I am Failing this article. Philroc (talk) 15:08, 20 January 2014 (UTC)

Hi Ankit Maity and Philroc, thanks for reviewing the article. Given the terse grading above and the extended exchange in which I gather something wasn't done correctly, I am bit unsure as to the next steps. My understanding is that for the article to regain GA status, the following would need to be addressed:

  • The lead needs to better summarize the content of the article
  • The citation needed tags need proper references

It seems like there might be other issues, but I cannot tell for sure. Do you have any further comments or helpful advice? Thanks, --Mark viking (talk) 01:46, 26 February 2014 (UTC)

Well, one reference of this article is an Internet post. Philroc (talk) 11:34, 26 February 2014 (UTC)


An ip-editor had written "This is of course nonsense." as the sections final sentence. It was was recently reverted as possible vandalism. The ip-editor was right. The whole section is utter nonsense. YohanN7 (talk) 21:10, 22 April 2014 (UTC)

Now removed. For reference, what was in the article is displayed below.YohanN7 (talk) 21:13, 22 April 2014 (UTC)


In fields as different as cultural geography, political theory and psychoanalysis, an increasing use of topology has attempted to consider space using metaphors of proximity, closeness, neighbourhood and transformation rather than simply distance. With its emphasis on holes and sutures and its attention for qualitative traits rather than quantitative properties of geometrical structures such as lengths, degrees, and areas, topology has offered crucial tools for critical investigations. This has allowed for consideration of complex structures in their totality, addressing elements of contiguity and transformation and producing new ways of representing and problematising subjectivity formations. Applications of topological structures like the Möbius strip have been used to illustrate a number of phenomena, including the formation of the unconscious in Lacanian psychoanalysis or the spatial conceptualisation of universalism in Islamic political theology.

Topology -Humanities[edit]

I can't see why this section has been removed. It makes perfectly sense to me, as it gives readers an idea of the practical application of topology in the Humanities (a reference that was regrettably missing in the page), providing also some useful reference, in the hope that new editors could integrate (rather than delete) the section. It seems to me that the ip-editor's comment that the section and the last sentence are 'nonsense' is completely unjustified. As far as I know, Lacan was well-known to use topology in his psychoanalitic theory of the unconscious. — Preceding unsigned comment added by Sesamo12 (talkcontribs) 08:38, 26 May 2014 (UTC)

Lacan may have used what Lacan called "topology". But no one really understands Lacan, so no one knows what he meant, assuming he did in fact mean anything. It seems very unlikely that it had much to do with the topic of this article. --Trovatore (talk) 08:57, 26 May 2014 (UTC)

I can hardly agree with the content and the form of this comment: 'no one really understands Lacan'. This is quite a superficial remark, and convinces me even more that the the removal of that section was unjustified and unhelpful. To point to the practical applications of topology in the humatities, including cultural geography, urban studies, etc. would help give a broader picture on topology, enriching this page, which by the way is the general page on topology as such, not topology AND math. Anyway, regardeless your thoughts on Lacan, it is against the spirit of wikipedia to censure things, removing sections only because according to you they express a different take or meaning on the topic of the page. Please, leave wikipedia being a place for the commons, and the commoning, where people can debate and confront their veiws, rather than deleting parts and contributions bluntly.--Sesamo12 (talk) 13:24, 26 May 2014 (UTC)

I would be happy for the article to discuss "practical applications of topology in the humanities" — if there were any. It's not impossible that there are, I suppose, though I don't know of any. A few postmodern mystifiers misusing the term, though, doesn't count. --Trovatore (talk) 18:47, 26 May 2014 (UTC)
very arrogant comment indeed by Trovatore --Sesamo12 (talk) 21:32, 26 May 2014 (UTC)
The article cited used the Moebius strip merely as an analogy. What would be required for such a section would be a scholarly reliable source explaining how topology is used (or misused a la Sokal) in those subjects, not a random paper that happens to use a concept from topology as a metaphor. Deltahedron (talk) 21:37, 27 May 2014 (UTC)
Whether one believes that Lacan's work is an important bridge between topology and the humanities or that his application of topology is only pseudo-scientific posturing, his work is notable and discussed in reliable sources. The sections Jacques Lacan#Writings and writing style and Jacques Lacan#Criticism reference multiple RS regarding his topological writings and their reception; there is an entire book, Lacan: Topologically Speaking, of commentary and criticism of his topological writings. I don't think it would be undue weight to mention (1) his work and (2) that it is a controversial application of topology.
In the broader context of humanities, a simple Google search shows a number of applications of topology to humanities, usually in the form of network connectivity relations that don't have a notion is distance, or are independent of it, e.g., [1], [2], and [3]. How these should be treated in this article depends on whether there is a good secondary source, like a review article, on the role of topology in these subjects. I have not yet found a general review of topology in the humanities, but there are such for topics such as corpus linguistics, see [4] and [5]. --Mark viking (talk) 22:20, 27 May 2014 (UTC)
How is it an application of topology at all? It's what he calls topology. Where does he do any actual math? Topology in the sense of this article is mathematics; any application of topology to the humanities is ipso facto an application of mathematics to the humanities. There are applications of mathematics to the humanities, but if you can't see that it's mathematics, then it's also not topology. --Trovatore (talk) 22:47, 27 May 2014 (UTC)

Animated example with donut[edit]

I thing that intermediate stages in animation of going from mug to doughnut is not a correct represantaition of continuous deformation, therefore are misleading. Compaire the Mugs 1. with closed top and 2. with open top. Are they same?

Yes. The cup part of the mug is an indentation, and is topologically the same as (homeomorphic to) a solid. For example, consider a "fat" hemisphere that opens upward, like a cup. That can be mapped downward into a "fat" pancake by a continuous bijection, and then mapped back upward to the hemisphere by the inverse bijection. The part of the cup that is topologically equivalent to the hole in the donut is the handle. Rick Norwood (talk) 12:56, 26 November 2014 (UTC)
PS Why is this header red? Does anyone know. And why are some headers black and others blue. The formatting looks the same. Rick Norwood (talk) 13:01, 26 November 2014 (UTC)
It's red because it's a link to an article which doesn't exist; blue would be a link to an article which does exist, and black is not a link. — Arthur Rubin (talk) 13:33, 26 November 2014 (UTC)

Thanks!Rick Norwood (talk) 15:05, 26 November 2014 (UTC)

Just for clarification. Those two mugs (with closed and open top) have different serfice areas. This is visualy apparent. Does it matter? (talk) 19:43, 26 November 2014 (UTC)
No, surface area doesn't matter. Two spheres of different sizes have different surface area, but they can certainly be continuously deformed into each other. -GTBacchus(talk) 19:48, 26 November 2014 (UTC)

In fact, the power of topology is that it applies in many situations where measures like length, area, and volume do not apply. It measures something more fundamental. Rick Norwood (talk) 20:53, 26 November 2014 (UTC)

First sentence defines topology as "...topological spaces."[edit]

Topology... is the mathematical study of shapes and topological spaces.

From page on 'Topological space': "In topology..."

Is there cyclic defining going on here? — Preceding unsigned comment added by (talk) 16:45, 7 May 2015 (UTC)

No, since the definition of a "topological space" is not defined using the term "topology". Paul August 16:49, 7 May 2015 (UTC)

Still, we should avoid the appearance of a circular definition.Rick Norwood (talk) 11:50, 8 May 2015 (UTC)

In general I don't think we need to worry too much about circularities in WP "definitions". The complaint at natural number and integer, in particular, was kind of a silly one, and in my opinion did not need to be addressed. The thing to keep in mind is that a WP definition is not like a mathematical definition. It is not intended to completely specify a class of thing, but just to let the reader know what the article is about.
This one is equally silly except for the the repetition topology/topological in the sentence itself. That repetition is not a logical problem, just a stylistic one, but it would be nice to address that. I have no immediate suggestion as to how to do it. --Trovatore (talk) 15:34, 8 May 2015 (UTC)

General vs point-set topology[edit]

OK, this is not a new issue, but I wonder if we can finally clarify it, maybe not once-and-for-all, but at least clearer than it's been.

I happened to notice this passage from the introductory section:

  • General topology establishes the foundational aspects of topology and investigates properties of topological spaces and concepts inherent to topological spaces. It includes point-set topology, which is the foundational topology used in all other branches (including topics like compactness and connectedness).

However, point-set topology, which is linked, is simply a redirect to general topology.

I know that in past discussions some editors have tried to draw a distinction between general topology and point-set topology, but I've never gotten a sense that there's really a clear agreed one to draw. Some editors have based it on the "level", but I've never been sure which topic is supposed to be "more advanced".

I guess you could argue that "general" topology includes pointfree topology, whereas point-set topology doesn't (if there are no points, how can there be pointsets?) but pointfree topology being a relatively small field, I have my doubts that most workers who talk about "general topology" or "point-set topology" are really making that particular distinction. I think the terms are used mostly as synonyms, with "general" being perhaps slightly more "modern" terminology.

I suppose my suggested fix for this particular passage is pretty simple; something like this:

  • General topology, also called point-set topology, establishes the foundational aspects of topology and investigates properties of topological spaces and concepts inherent to topological spaces. It defines the basic notions used in all other branches of topology (including concepts like compactness and connectedness).

So I know, kind of a lot of words for a change I could just have made boldly, but if there really is a distinction that's generally understood in the field between general and point-set, then maybe someone could point it out. In the meantime, I think I'll go ahead and put in my suggested change. --Trovatore (talk) 08:44, 6 September 2016 (UTC)

Back in the stone age–when I was in graduate school–general topology and point-set topology were considered synonyms. More particularly, "general topology" was used to differentiate the field from "algebraic topology" (other flavors of topology were never brought up in this dichotomy, even though there were some specialists in those areas around). The usual locution was "General (point-set) topology ..." with the parenthetical remark, in a lower voice, thrown in for clarification. So, I support your change. --Bill Cherowitzo (talk) 21:17, 6 September 2016 (UTC)

Imperfect topology not mentioned here[edit]

Imperfect topology, under some critical conditions, allows breaking.

we can avoid that with QFT, but mention it! — Preceding unsigned comment added by 2A02:587:410E:4500:AD6F:A2A0:C913:453C (talk) 17:23, 5 November 2016 (UTC)
Could you explain what you're talking about, please? --Trovatore (talk) 03:19, 6 November 2016 (UTC)

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