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nLab > Latest Changes: closed subgroup

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeApr 3rd 2021
    • (edited Apr 3rd 2021)

    Am giving this its own little stub entry, so that I don’t have to type “[[closed subspace|closed]] [[topological group|topological]] [[subgroup]]” all the time.

    Also, it goes nicely along compact subgroup.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeApr 3rd 2021

    Added a subsection about localic subgroups:

    Localic subgroups

    Any subgroup of a localic group is automatically closed. See there for more information.

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeApr 3rd 2021
    • (edited Apr 3rd 2021)

    [ deleted ]

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeApr 4th 2021
    • (edited Apr 4th 2021)

    Thanks!

    I have made it read “localic subgroup”, have added pointer to the theorem, and have added pointer back from there to here.

    diff, v3, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeApr 4th 2021

    added statement and proof (here) that isotropy subgroups of continuous actions on T1-space are closed subgroups

    diff, v4, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeApr 11th 2021

    added the observation that open subgroups are closed (copied over from topological group)

    diff, v7, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeApr 12th 2021

    added statement of Cartan’s closed subgroup theorem, which I’ll give it’s own little entry now

    diff, v8, current

1 to 7 of 7

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