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nLab > Latest Changes: main separation axioms -- as lifting properties

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  1. A page with diagrams representing separation axioms T0-T4 as lifting properties, to be included into the separation axioms.

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeOct 16th 2021
    It would help if one could put several diagrams next to each other, not below each other. I do not know how to do this..
    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeOct 17th 2021

    As far as I know it is not currently possible to arrange TikZ-diagrams next to each other inside nnLab entries.

    But an easy hack might be to group tikzcd-diagrams inside a tikzpicture-environment. Let me try that out in the Sandbox…

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 17th 2021
    • (edited Oct 17th 2021)

    Okay, I checked and it does not currently work here to have tikzcd-environments inside tikzpicture-environments. But the error message suggests that the only reason is that the tikzcd-package isn’t being loaded when TikZ is called via tikzpicture. If that’s the case, Richard would be able to easily change this. I’ll drop a note on this in the thread “bugs and feature requests”: here.

    • CommentRowNumber5.
    • CommentAuthorGuest
    • CommentTimeOct 19th 2021
    Many thanks!

    Do you think the diagrams in this page are clear to the intended reader, with the little explanation provided ?
    If yes, should I add !include this page alongside the table of separation axioms , in the pages for [[normal space etc ?
    Alternatively, I could add an appropriate diagram + this short explanation + link to separation axioms as lifting properties
    at the pages for normal, regular, etc spaces ?

    What would be most appropriate ?
    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeOct 19th 2021
    • (edited Oct 19th 2021)

    I see. Okay, I have edited the entry a little, to make it work well as an !include-page:

    • added a section header and inside it Proposition-environments for various claims,

    • expanded out the lead-in text a little to make it more inviting,

    • gave each of the diagrams a brief text saying what it’s about, with a pointer to the corresponding separation axiom.

    Now to include this as a Properties-section in the relevant entries, to add the following line at the desired spot

      [[!include main separation axioms -- as lifting properties]]

    diff, v2, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeOct 19th 2021

    Now I have !include-ed the section as a Properties-subsection into the relevant entries

    (e.g. at Hausdorff space, see the announcement here).

    Except for the case of T 1T_1, as that is currently redirecting just to separation axiom. It might be good to remove that redirect and instead make T1-space a page.

  8. Thanks, I wouldn’t have been able to write that well. Seems the separation axioms work is going to an end…

    I shall try to make a page for T1.

    Anonymous

    diff, v3, current

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