Talk:Compactification (mathematics)

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Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. needs refs, try finding some here.--Cronholm144 23:23, 28 May 2007 (UTC)

As far as i can tell, compactification of extra dimensions in string theory has nothing to do with Stone-Čech compactification in point set topology. In the first case, we simply choose a compact manifold (e.g. CY₃) to replace a noncompact one, turning the spacetime M₄xR⁶ into M₄xCY₃ by fiat. We do not require that there exist an isometry (indeed, there will not be one), or even a continuous embedding from R⁶ into CY₃, nor do we require any uniqueness. In the second case, given a noncompact topological space, we look for a (in some instances unique) compact space with a continuous embedding.

I think they should be in separate articles. The are simply not related. Comments?

Well, no. The Stone-Cech is the most complicated compactification, as the one-point is the simplest. Compactification with no continuity condition would be a strange thing (one can Stone-Cech a discrete space if one really has to ...); I suspect that the string theory usage is driven by certain motivations that could be explained, but if you are talking about non-compact to compact manifolds, there must be quite an amount of topology to carry over.

So, some examples of compactifications would add to the article.

Charles Matthews 08:33, 27 May 2004 (UTC)

You know, for some reason, i thought i was looking at an article entitled "Stone-Cech Compactification". Now i see that the article is titled simply "Compactification". This is fine then. Clearly stringy compactification doesn't belong in an article on stone-cech, but i was mistaken. I think i must have seen the Redirect notice and thought it was the title Lethe