Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: compact connected space

Bottom of Page

1 to 3 of 3

  1.  

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

    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

1 to 3 of 3

  1.