Talk:Space (mathematics)

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 Definition A set with some added structure, which often form a hierarchy, i.e., one space may inherit all the characteristics of a parent space. [d] [e]

Lay explanation of space concepts

An inspiring video on Euklidean space, spherical space and hyperbolic space, coral reefs and crochet that may be of relevance here. --Daniel Mietchen 01:18, 25 July 2009 (UTC)

I see, thank you. However, this could be better used on the "Non-euclidean geometry" article rather than here. Boris Tsirelson 17:25, 25 July 2009 (UTC)

Please improve

It seems, I did my best. Now please improve it. (Especially, my poor English... I am not a native English speaker.) Boris Tsirelson 19:57, 28 July 2009 (UTC)

The name of the article

I just want to mention that I noticed your work on Space (mathematics) which is now a quite substantial article. I have not reacted until now because, unfortunately, I have not yet read it thoroughly. Probably it needs only some proof reading and polishing before it is ready for approval. But since it is a quite ambitious survey, I think that the title should be changed to reflect this (Abstract space?, I'm not yet sure.) and leave "Space (mathematics)" for a more basic introduction.

Peter Schmitt 22:40, 4 October 2009 (UTC)

Thank you for the high opinion; I am glade you like it.
About the title: as we know (and non-mathematicians maybe do not know), the word "space" in mathematics is mostly used in such combinations as "linear space", "topological space" etc. Thus, it is "abstract" by default. The other usage could be rather "Space (solid geometry)" or something like that? Boris Tsirelson 10:05, 5 October 2009 (UTC)
Here is another option: one article "Space (elementary mathematics)", the other "Space (advanced mathematics)". Boris Tsirelson 19:17, 5 October 2009 (UTC)
Thanks for moving to this talk page. I was not going to discuss the article on your talk page. (The first message was not intended to start a discussion, I just wanted to inform you.)
Concerning the title: There is no hurry. I hope to go through the article soon. (I have to confess that I don't know the term "solid geometry" -- it lets me think of the geometry of solids.) Peter Schmitt 22:50, 5 October 2009 (UTC)

Inline references

As far as I understand, detailed inline refs are encouraged in Wikipedia but discouraged here. The Wikipedia version of this article contains detailed inline refs throughout the section "History". Is it a good idea to do the same here? Boris Tsirelson 19:24, 5 October 2009 (UTC)

Ah, I did not realize that you put a parallel version on WP. Am I correct that you first wrote it here, so that no template is needed?
There is no rule that for every statement there should be an explicit reference. On the contrary, the WP style of citations is discouraged. But practice varies and depends on the topic (and I think that different styles should be possible). The general policy (as I understand it) is to write as one would write for a publication in one's field. My personal opionion is that, in most cases, it is sufficient (and preferable) to have a list of sources in the bibliography (may be separated from reading suggestions). You say several times "according to Bourbaki" -- so it is clear that it is a main source. If, for some reason, a precise citation is wanted (e.g., for a verbatim citation) than I would probably add (Bourbaki, in the text (or, depending on the situation, in a reference).
Just an idea: Would "Space (Bourbaki)" fit? Peter Schmitt 23:24, 5 October 2009 (UTC)
The WP version is made later, and the credit to Citizendium is given there. If the CZ article will be approved, WP will treat it as a "reliable source".
No, "Space (Bourbaki)" makes impression that this is an approach of a minority (Bourbaki and others). But it is the mainstream! Boris Tsirelson 05:55, 6 October 2009 (UTC)
The contribution of Bourbaki is, a definition of a mathematical structure in general (with related technical definitions and lemmas), of which all these spaces (and many algebraic notions) are special cases. However, that technical definition is not even mentioned in my text. Thus, my text is not Bourbaki-ish; I think so. Boris Tsirelson 06:20, 6 October 2009 (UTC)
Sorry, Boris, this last remark was not fully serious. Peter Schmitt 09:01, 6 October 2009 (UTC)
Alas, I recognize humor only by the symbol :) Boris Tsirelson 11:59, 6 October 2009 (UTC)
No harm done, I hope. ( ;-) ) Peter Schmitt 23:36, 6 October 2009 (UTC)


I still think that "Space (mathematics)" is not the right name. The article does not deal with all uses of "space" in mathematics, and it isn't an introduction to Space (geometry) either. What do you think of "The mathematical concept of space" or "Evolution of the mathematical concept of space"? Have you a better idea? --Peter Schmitt 23:16, 9 August 2010 (UTC)

We shall have to be careful with final copyediting so that I stay able to approve it. --Peter Schmitt 23:19, 9 August 2010 (UTC)

'The article does not deal with all uses of "space" in mathematics' — we know that an article never covers all, but the question is, whether it covers the most relevant matters. Which important uses of "space" in mathematics missing here do you mean?
"The mathematical concept of space" — is it really different in meaning from "Space (mathematics)"? I do not feel why it could solve the problem. And surely no one will seek exactly this name... the more so, even longer "Evolution of the mathematical concept of space"...
However, let us discuss it another way. Do you agree that an encyclopedia should contain such entries as "space (mathematics)" and/or "space (geometry)"? What should these entries contain, in your opinion? Disambiguation pages? Articles? Which kind of articles? I do not insist "my" article to be just here, but I want to see a reasonable planned configuration containing it. Boris Tsirelson 06:15, 10 August 2010 (UTC)
Well, your message of Oct 4, 2009, is a partial answer: 'and leave "Space (mathematics)" for a more basic introduction'. OK, let us write this more basic introduction with link(s), and so, I'll understand what do you want to see. Boris Tsirelson 06:22, 10 August 2010 (UTC)
We already have Space (disambiguation) (with redirection from Space, of course). What do you think of it? Some readers will probably seek just "Space", but there is a chance that others will try "Space (mathematics)" or "Space (geometry)" from the start. Or not? Boris Tsirelson 06:26, 10 August 2010 (UTC)
I have to think about your arguments. We need not bother now if we think that changing the name of an approved page is acceptable. --Peter Schmitt 09:26, 10 August 2010 (UTC)
A good question to constables... Boris Tsirelson 11:28, 10 August 2010 (UTC)
This is not a question what is allowed now (it certainly would be possible with a reapproval, at most). It is rather a question what official policy should be. --Peter Schmitt 11:33, 10 August 2010 (UTC)
Anyway, our good practice is, to think before the approval, isn't it? :-) Boris Tsirelson 11:40, 10 August 2010 (UTC)
That's why I started with this question ;-) --Peter Schmitt 16:04, 10 August 2010 (UTC)


"geometry is a mathematical truth". Rather: corresponds to a collection of mathematical truths, is a set of math.truths, or similar? --Peter Schmitt 16:00, 10 August 2010 (UTC)

Regretfully, the Bourbaki's history book is returned to the library. I guess that I did my best not to modify formulations taken therefrom. I know I cannot speak such a high-style English; thus I prefer to borrow it from book(s). I'll try to take the book again. Boris Tsirelson 16:16, 10 August 2010 (UTC)
I did not realize that these are citations from Bourbaki, and I did not mean the English. I meant the logic of the sentence: Is geometry a statement, a single truth? --Peter Schmitt 17:05, 10 August 2010 (UTC)
Not quite citations... Anyway, I did "geometric theorems are mathematical truths". (Though, it is not impossible to treat a theory, in particular geometry, as one big truth: just the conjunction of all axioms and theorems.) Boris Tsirelson 19:21, 10 August 2010 (UTC)

Google juice

This article is currently #6 in the Google search for "Space (mathematics)" (with or without the quotes). Boris Tsirelson 19:48, 11 October 2010 (UTC)