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nLab > Latest Changes: preconvergence space

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  1. Page created, but author did not leave any comments.

    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 5th 2022

    I have adjusted wording and hyperlinking of the lead-in sentences, for readability.

    It would be good for the entry to cite some references.

    diff, v4, current

  3. Added the definition of preconvergence space directly in terms of nets without using filters

    Anonymouse

    diff, v6, current

  4. In the existing mathematical literature on topology and convergence, preconvergence spaces have an requirement that they satisfy the isotone condition; see i.e.

    • Dolecki, Szymon; Mynard, Frédéric (2016). Convergence Foundations Of Topology. New Jersey: World Scientific Publishing Company. ISBN 978-981-4571-52-4. OCLC 945169917.

    • Dolecki, Szymon (2009). Mynard, Frédéric; Pearl, Elliott (eds.). “An initiation into convergence theory”. Beyond Topology. Contemporary Mathematics Series A.M.S. 486: 115–162. (pdf)

    Are there any references which use “preconvergence space” for this space without the isotone condition?

  5. In Non-symmetric Convenient Topology and its Relation to Convenient Topology the author Gerhard Preuss defines a “preconvergence space” to be this other structure:

    • a preconvergence space is a preuniform convergence space which is ‘generated’ by its preconvergent filters

    which doesn’t have anything to do with the other definition by Dolecki and Mynard etc.

    See also,

  6. John Baez suggested that I add these references to the article even though none of the definitions of a preconvergence space found in the articles are the same as the definition already given in the article.

    diff, v8, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 18th 2024

    Madeleine, I am not sure what you are trying to do (or what somebody else is making you do), but if the entry needs fixing there is no need to hesitate: After all, this is one of the notorious Anonymous edits — you know the story.

    The first thing I asked (in #2) when the entry was anonymously created, in 2002, is for references supporting its claims. As usual, this request was ignored by the entry’s author.

    It sounds now like you have the references and that they disagree with our notorious anonymous contributor. If so, by all means, let’s fix whatever needs fixing.

  8. I went ahead and edited the article with a correct definition of preconvergence spaces.

    diff, v9, current

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeNov 18th 2024

    Good, thanks!

    • CommentRowNumber10.
    • CommentAuthorJohn Baez
    • CommentTimeNov 18th 2024
    • (edited Nov 18th 2024)

    By the way, I didn’t “make” Madeleine do anything. She came up with a bunch of references for “preconvergence space” but was worried because the definition used in those references did not match the definition given on the nLab. I suggested that she take suitable actions to improve the situation after consulting the nForum. I’m glad she did.

  11. Sorry for the bad wording on my part.

1 to 11 of 11

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