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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeSep 3rd 2012

    tried to polish topological base a little.

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeSep 5th 2012
    • (edited Sep 5th 2012)

    I have added the concept of a subbase of topology and fundamental system of neighborhoods at a given point as well as mentioning the character of a topological space and separability axiom (first one, if my memory is right). Please check, I wrote quickly from my memory.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeSep 5th 2012
    • (edited Sep 5th 2012)

    I made your

       Definition
    

    a

     +-- {: .num_defn}
      ###### Definition
    

    so that it appears in line with the rest.

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeSep 5th 2012
    • (edited Sep 5th 2012)

    I thought it was called the first axiom of countability. Doesn’t “separable” mean instead that there is a countable dense set of points?

    • CommentRowNumber5.
    • CommentAuthorTobyBartels
    • CommentTimeSep 6th 2012
    • (edited Sep 6th 2012)

    Yes, Mike’s memory agrees with mine. I’ll edit it. Zoran, please complain if we are wrong.

    • CommentRowNumber6.
    • CommentAuthorTobyBartels
    • CommentTimeSep 6th 2012

    This page should really just be about the concept in topological spaces, with a pointer to the much more extensive articles on bases for Grothendieck topologies. I am going to boldly change this too. Urs, please complain.

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2012

    Urs, please complain.

    No, why? Go ahead.

    • CommentRowNumber8.
    • CommentAuthorTobyBartels
    • CommentTimeSep 7th 2012

    Good!

    • CommentRowNumber9.
    • CommentAuthorzskoda
    • CommentTimeSep 7th 2012

    Yes, the first axiom of countability. I mistranslated to English, coupled with weak memory :) The page looks quite good after all your interventions !

    • CommentRowNumber10.
    • CommentAuthorTobyBartels
    • CommentTimeSep 7th 2012

    I’m glad that everybody is happy!

    Ironically, separability got into the page anyway, in the example showing the base that proves that separable metric spaces are second-countable.

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