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nLab > nLab General Discussions: disambiguation problem: formal space

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 10th 2010

    we need to resolve a problem with current redirects:

    currently formal space redirects to formal topology.

    I happen to know “formal space” in the sense given at formal dg-algebra: a topological space such that its dg-algebras of Sullivan forms is a formal dg-algebra. I think this is very wide-spread and classical use of the term. But it means something different than the sense in which it is used at formal topology.

    I have now at least added a disambiguation at the top of formal topology. But I am wondering if we should not redirect and dismbiguate the other way round. Isn’t “formal space” in the dg-algebra sense much more common and well established terminology than “formal space” in the sense of formal topology?

    • CommentRowNumber2.
    • CommentAuthorTobyBartels
    • CommentTimeSep 11th 2010

    I don’t know what’s more established. In an anoymous Google search for "formal space", the top hit matches your meaning, while the second matches my meaning. None of the other top ten hits match your meaning, while several of them match my meaning. Going through a few more pages, both of our meanings are well represented. There are two articles on the math arXiv with ‘formal space’ in the title, one for each of our meanings. Searching for "formal topological space" gives similar results.

    I have to admit that your usage seems odd to me. Do we normally add adjectives to ‘space’ or ‘topological space’ to match a space’s algebra of Sullivan forms? (If the dg-algebra of Sullivan forms is simple, for example, do we call it a ‘simple space’?) If it is specifically rational spaces whose homotopy type is determined by their Sullivan forms, I would be inclined to say ‘formal rational space’ instead. But I admit that people don’t seem to say that much (although I got a few Google hits for it.)

    By the way, I was thinking of renaming formal topology to formal space, since the latter seems to be used more than the former. This is probably a bad idea now. The term is also used in a few different ways in the literature (the most extreme being a simple synonym for ‘locale’), which I am in the process of clearing up for myself so that I can add them to the article. It may be that the best use of formal space is as a page that explains the different meanings, linking to formal topology and formal dg-algebra, as well locale and possibly geometric theory. If it would help, I can hurry up on straightening out the different meanings in formal topology.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 11th 2010

    Hi Toby,

    thanks for this survey. I agree that “formal spaace” in “my sense” is bad use of terminology. But it is ancient. (As so many bad things ;-)

    Okay, so I wasn’t aware that “formal space” in “your sense” is wide-spread at all. So that’s good to know.

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeSep 11th 2010

    Perhaps some page on the various uses of ’formal’ might be useful. My question would then be ’what should go in it?’

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