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nLab > Latest Changes: Cheng space

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  1.  
    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJul 31st 2019

    Thanks to a Guest comment here I looked at this page for essentially the first time, and realized that it’s one more thing that’s naturally done in linear constructive mathematics (“complemented subsets” or “disjoint pairs” are the elements of the linear powerset).

    One question: this page says that the disjoint pairs form a “Boolean rig”, but that doesn’t seem right to me. A Boolean rig would, I presume, lack a negation operation entirely; but here we do have an involutive “negation” even though it’s not the “additive inverse”. I would say that the disjoint pairs form a De Morgan algebra, and in fact more generally a *\ast-autonomous lattice. Am I misinterpreting the intended meaning of “Boolean rig”?

    Also, what is the “Handbook of Constructive Analysis” referred to (as a graylink from Bishop \& Bridges)? I can’t find it on google.

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorRodMcGuire
    • CommentTimeAug 1st 2019

    Also, what is the “Handbook of Constructive Analysis” referred to (as a graylink from Bishop \& Bridges)? I can’t find it on google.

    Where are you getting that title from?

    I presume the referernce is just to

    Bishop, Errett and Douglas Bridges, 1985. Constructive Analysis. New York: Springer. ISBN 0-387-15066-8.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeAug 1st 2019

    Second paragraph of the idea section of the page:

    Some of the [[abstract nonsense]] below is original research (by [[Toby Bartels]] and [[Todd Trimble]]), but based heavily on Cheng\'s work as described in [[Handbook of Constructive Analysis|Bishop & Bridges]].

  4. I added the reference to the Bishop & Bridges textbook mentioned in the introduction of this article.

    diff, v5, current

  5. I also added the Bishop Cheng textbook on constructive measure theory to the references.

    diff, v5, current

    • CommentRowNumber6.
    • CommentAuthorTobyBartels
    • CommentTimeAug 25th 2024

    Sorry Mike, that should have been ‘Foundation’, not ‘Handbook’. (Although strictly speaking, ‘Foundation’ is only in the title of the first edition, by Bishop alone; Bridges shortened the title for the revised edition, which is the one that includes the material by Cheng.)

    Madeleine (who brought this to my attention) has already fixed the article; thanks, Madeleine.

1 to 6 of 6

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