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nLab > Latest Changes: proper map

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeMay 12th 2017

    For better readability, I have split off proper map (topology) from proper morphism (general) and added disambiguation. Added classes of examples at proper map.

  2. fixed typo “cncepts” -> “concepts”

    Anonymous

    diff, v4, current

  3. Cleanup definition of proper.

    Aniruddh Agarwal

    diff, v7, current

  4. Complete rewrite.

    Damien Lejay

    diff, v8, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeFeb 13th 2023

    did a fair bit of adjustment (wording, layout, formatting, typesetting) in particular so that the “complete rewrite” interacts with the material that was there before.

    diff, v9, current

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 13th 2023

    Typos fixed

    diff, v10, current

  7. Add a counter-example.

    Damien Lejay

    diff, v11, current

  8. Add another description as “continuous family of compact fibres”.

    Damien Lejay

    diff, v12, current

    • CommentRowNumber9.
    • CommentAuthorDmitri Pavlov
    • CommentTimeFeb 14th 2023

    Added the much needed references:

    References

    One of the early reference on proper maps is

    • Nicolas Bourbaki, Topologie Générale (Éléments de Mathématique, Livre III), Chapitres 1 à 2. Second Edition, 1951. Actualites Sci. Ind. 1142, Hermann, Paris.

    A considerable expanded treatment is given in the third edition, see Chapter I, Section 10:

    • Nicolas Bourbaki, Topologie Générale (Éléments de Mathématique, Livre III), Chapitres 1 à 2. Third Edition, 1961. Actualites Sci. Ind. 1142, Hermann, Paris.

    English translation of the 1971 edition:

    • Nicolas Bourbaki, General Topology (Elements of Mathematics), Chapters 1–4. Springer, 1987.

    The localic version of proper maps was introduced by Johnstone:

    • Peter Johnstone, Factorization and pullback theorems for localic geometric morphisms, Univ. Cath. de Louvain, Sem. de math, pure, Rapport no. 79.

    • Peter Johnstone, The Gleason cover of a topos, II, Journal of Pure and Applied Algebra 22:3 (1981), 229–247. doi.

    diff, v14, current

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeFeb 15th 2023
    • (edited Feb 15th 2023)

    Thanks!

    have added doi:10.1007/978-3-642-61701-0 for Bourbaki’s book

    fixed the link doi:10.1016/0022-4049(81)90100-6 (for “The Gleason cover…”): Since the url has unescaped parenthesis, it does not work with the [link](url)-syntax, unfortunately. One can escape the parenthesis if one remembers or bothers to look up the respective codes, otherwise one can fall back to HTML syntax <a href="url">link</a>.

    Do we have any hyperlink for

    • Factorization and pullback theorems for localic geometric morphisms, Univ. Cath. de Louvain, Sem. de math, pure, Rapport no. 79.

    ?

    diff, v15, current

    • CommentRowNumber11.
    • CommentAuthorDmitri Pavlov
    • CommentTimeFeb 15th 2023

    Re #10:

    In the second paper, Johnstone writes:

    Parts of the paper (in particular the contents of Section 1) appeared in a preliminary form in [16]; I am grateful to Francis Borceux for providing me with the incentive to write [16].

    where [16] is the paper “Factorization…” and Section 1 is the section about proper maps.

    So I think it is safe to say that the “Factorization…” paper is just a preprint that was never properly published (as indicated by “Rapport no. 79”), and its mathematical content relevant to proper maps appeared in Johnstone’s 1981 paper, which was submitted in 1979. So there is really no point in citing the “Factorization…” paper other than to move the priority date a few months back (not that it is under dispute anyway).

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeFeb 15th 2023

    I see, thanks. So I have added brief commentary (here) to make this clear and save the reader the headache of hunting for that rapport.

    diff, v16, current

  13. Add another equivalent characterization of properness, useful to show the comparison between proper maps of topological spaces and proper maps of locales. Add a proposition comparing the two notions.

    Damien Lejay

    diff, v17, current

  14. Add a warning about inconsistent terminology

    Damien Lejay

    diff, v17, current

  15. Move the remark on inconsistent terminology to another page.

    Damien Lejay

    diff, v17, current

1 to 15 of 15

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