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I am working on giving the entry on topology a section Introduction. This section is meant to provide persons with some background in, say, analysis, but otherwise with no idea of topology, briefly with some basic ideas. The basic definition, some pictures, the basic idea of how to use topological invariants in very simple examples, maybe culminating in an outline of the fundamental group and its relation to covering spaces. Not done yet.
Okay, I now have a stable version of
It starts from motivating the concept of a topological spaces, considers homeomorphisms, motivates the use of topological invariants to distinguish topological spaces, and ends with the statement of the fundamental theorem of covering spaces and some brief comments on how that helps with computing fundamental groups.
The idea is not to make this much longer, to retain its introductory nature. But of course if you feel something really needs to be added, please let me know.
I have added a bunch of illustrating pitures. More could be be added, but I need to pause now for a moment.
added more illustrations to Topology – Introduction
Wow, this is really extensive!
I have also made a German translation of the page. For the moment this is at Topologie.
(Maybe not to collide with the capitalization convention on the Lab I should rename this to, maby “topology (deutsch)” or the like. (?))
I don’t think you have to worry about the capitalization convention. If the German convention is to capitalize nouns, then I think it makes sense to stick with that.
Is there a reason for omitting a lot of commas that are obligatory by standard German punctuation?
No reason, no. It’s a fair bit of work to translate such a page, with all the hyperlinks retained etc. I just fixed a bunch more typos. There are more left. If you happen to read through it carefully enough to spot more, you could do me and every reader after you a big favor by hitting “edit” and fixing them right away. Thanks!!
By the way, is there a reason that in many articles (Paul Hertz, infinite judgement) commas are separated by two spaces (one on each side)? Even according to French rules this is not sound. This always causes precompiler errors in my brain! (much worse than simply grammatically wrong commas)
What I seem to have noticed is that the use of underscores to create emphasis sometimes doesn’t work right when one is placed next to a comma, and so people have been creating an extra space to address that.
Personally, I’ve been avoiding using underscores for this reason, and now use asterisks to create an italicized font. This never seems to run into the comma problem.
I just went in to fix the Paul Hertz article.
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