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    • CommentRowNumber1.
    • CommentAuthorTobyBartels
    • CommentTimeAug 22nd 2012

    Another new article: sequence space. I await the inevitable report that this term is also used for other things.

    • CommentRowNumber2.
    • CommentAuthorMark Meckes
    • CommentTimeAug 28th 2012

    You certainly use the term in the way I expected, but I take issue with the statement “The name ‘sequence space’ is not often encountered”. Personally, I encounter that name all the time

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2012

    I have added a link to the entry from the “Important subclasses”-section at topological vector space, but probably this deserves to be listed more systematically. Somehow.

    • CommentRowNumber4.
    • CommentAuthorTom Leinster
    • CommentTimeAug 28th 2012

    I added the synonym c00 for cc.

    I entirely don’t get the point about versus cb. The definitions seem to me to be word-for-word identical. (Am I missing some tiny change?) It says “two different ways of thinking about the same thing”, but I see literally no difference apart from the change of name.

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeAug 28th 2012

    Personally, I encounter that name all the time

    Good, maybe it is not such an obscure name, just left out of my education.

    I entirely don’t get the point about versus cb. The definitions seem to me to be word-for-word identical. (Am I missing some tiny change?) It says “two different ways of thinking about the same thing”, but I see literally no difference apart from the change of name.

    One way is as the culmination of the sequence (lp)0<p<, the other way is as the culmination of the sequence (cc,c0,c). Note that when we generalise N from a set to a non-discrete space (and start using capital letters for some reason), the two notions diverge. (I’ll add something about this to the article.)

    • CommentRowNumber6.
    • CommentAuthorMark Meckes
    • CommentTimeAug 28th 2012

    To paraphrase something I once heard in a talk, the name “sequences spaces” is well-known, in the usual sense of “well-known among those who know it well”.

    • CommentRowNumber7.
    • CommentAuthorTom Leinster
    • CommentTimeAug 29th 2012

    Thanks for the clarification, Toby. I sort of see the point, but the trouble is that I don’t see in any precise sense what progression is happening in the sequence (cc,c0,c,cb). So what you’ve written is almost as mysterious to me as if it had been the following:

    We write A for the category of abelian groups: xy=yx for all x and y. […] We write B for the category of abelian groups: xy=yx for all x and y. Indeed, A=B, two different ways of thinking about the same thing. (But they generalise differently.)

    • CommentRowNumber8.
    • CommentAuthorTobyBartels
    • CommentTimeAug 29th 2012

    Would that make more sense if, later in the article, there was a section on generalisations where they did indeed generalise differently?

    • CommentRowNumber9.
    • CommentAuthorTom Leinster
    • CommentTimeAug 30th 2012

    Not sure. It’s probably best to just ignore me and carry on. It was only a niggle anyway.