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nLab > Latest Changes: hyperstonean space

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeMay 27th 2020

    Created.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDmitri Pavlov
    • CommentTimeApr 14th 2021

    Added:

    Hyperstonean locales

    Hyperstonean locales can be defined as Stonean locales that admit sufficiently many normal valuations.

    Assuming the axiom of choice, Stonean locales are spatial, so the category of hyperstonean locales is equivalent to the category of hyperstonean spaces.

    diff, v5, current

    • CommentRowNumber3.
    • CommentAuthorDmitri Pavlov
    • CommentTimeApr 20th 2024

    Added:

    Hyperstonean cover

    Given a compact Hausdorff space XX, its hyperstonean cover is defined as a continuous map of compact Hausdorff spaces

    hX→XhX \to X

    that under the Gelfand duality corresponds to the canonical inclusion C(X)→C(X) **C(X)\to C(X)^{**} into the double dual.

    The hyperstonean cover of a compact Hausdorff space is introduced in

    • J. Flachsmeyer, Topologization of Boolean algebras, General Topology and Its Relations to Modern Analysis and Algebra IV, Lecture Notes in Mathematics 609 (1977), 81–97. doi.

    diff, v7, current

    • CommentRowNumber4.
    • CommentAuthorDmitri Pavlov
    • CommentTimeApr 20th 2024

    Added:

    A bibliography of hyperstonean covers can be found in

    • V. K. Zaharov, Hyperstonean cover and second dual extension, Acta Mathematica Hungarica 51:1-2 (1988), 125-149. doi.

    diff, v7, current

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