Not signed in (Sign In)

Start a new discussion

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 beauty bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus graph graphs gravity group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homology homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory kan lie lie-theory limit limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monoidal monoidal-category-theory morphism motives motivic-cohomology newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pasting philosophy physics planar 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-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).
    • CommentRowNumber1.
    • CommentAuthorTodd_Trimble
    • CommentTimeDec 30th 2016

    I saw tube lemma, and decided to bulk it up.

    Many books (such as the famous topology text by Munkres) give proofs which involves multiple subscripts and multiple choices; I’ve written arguments to mostly eliminate that.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMay 11th 2017
    • (edited May 11th 2017)

    Coming back to this, now that we have closed-projection characterization of compactness: i have cross-linked the entry with tube lemma.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 11th 2017

    And I have made explicit in both entries (here and here) the direct proof of the tube lemma via the closed-projection characterization.

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 11th 2017

    Of course the tube lemma was effectively proved within the proof of proposition 1.2. But it’s good to mention explicitly.

    More categorically, the tube lemma becomes the statement that for XX compact, the map π:P(Y×X)P(Y)\forall_\pi: P(Y \times X) \to P(Y) takes opens to opens, as mentioned in point 5. of the Variant proofs section.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMay 11th 2017

    I have added what you just said as a remark to the entry, right before and right after the statement and proof here.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)