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nLab > Latest Changes: compact connected space

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    Anonymous

    v1, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 18th 2022
    • (edited Jun 18th 2022)

    The “Definition” that was offered (now here) is clearly not the definition that an entry of “compact connected space” should advertise without further commentary.

    Also, that paragraph is at best a definition of “connected”, not of “compact”. I left a question mark to indicate that something seems amiss.

    Also, what is the reader to make of the pointer to

    • Paul Taylor, (2010). “A lambda calculus for real analysis”. In: Journal of Logic & Analysis 2.5, pp. 1–115 (cit. on pp. 4, 71–72).

    ?

    diff, v2, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 18th 2022
    • (edited Jun 18th 2022)

    Looking into the reference by Taylor now.

    Have added links to the file:

    Have removed

    (cit. on pp. 4, 71–72)

    from the bib-item, as this was copy-and-pasted verbatim from Mike’s document but makes no sense outside of it.

    Looking at Def. 13.2 by Taylor now, I see what the problem here is:

    Taylor is speaking in constructive mathematics, where the usual equivalent definitions of “connectedness” may not agree. So he chooses to call one of them “overt connectedness” and the other “compact connectedness”.

    Therefore I have moved this material to connected topological space into a new Subsection Constructive definition (see the discussion thread there) and have left here only a brief disambiguation line.

    diff, v3, current

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