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nLab > Latest Changes: category of topological spaces

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 1st 2016
    • (edited Apr 1st 2016)

    I am starting to add statement and discussion of basic properties of TopTop to Top. Spelled out the basics about limits and colimits, added some basic examples, some first remarks on the characterization over SetSet, etc.

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 1st 2016

    I thought the fact that TopTop is a topological category over SetSet, which is the subtext of Definition 1, needed to be highlighted more (it was mentioned but buried deep in the article), so I put in emphasis at the top of that subsection. I also changed the first occurrence of “set” in Definition 1 to “class”, because that’s actually an important nuance in the general theory of topological categories.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeApr 1st 2016

    Thanks!

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 5th 2016

    Added more exposition to the list of examples of colimits at Top, pushouts as “attaching spaces”, and included a graphics as illustration.

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeApr 5th 2016

    There’s a glitch in Example 6. You want to say “quotient topology”, not “subspace topology”, and remove reference to the earlier example. You may want to insert (prior to this) “quotient topology” as another example, an example where you need to use a final topology.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 5th 2016

    Thanks! Fixed now.

    (I had had “quotient topology” added as an afterthought to Example 1 “subspace topology”, but better to separate it.)

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 14th 2017
    • (edited Jun 14th 2017)

    I have spelled out in the subsection Universal constructions the example of the union of two open or to closed subspaces being a pushout in TopTop (here)

1 to 7 of 7

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