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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 nLab 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 T1, 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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