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: join of topological spaces

Bottom of Page

1 to 15 of 15

  1.  
    • CommentRowNumber1.
    • CommentAuthorTim_Porter
    • CommentTimeApr 4th 2019
    • (edited Apr 4th 2019)

    Added some more general references to work on topological joins.

    diff, v8, current

    • CommentRowNumber2.
    • CommentAuthorGuest
    • CommentTimeMay 6th 2022

    I have some edits for this page (https://pastebin.com/L7NTe7d3), but they keep getting rejected by the spam filter; could anyone tell me what’s wrong with them?

    Intended edit comment:

    Removed the incorrect quotient space description of X⋆YX\star Y (which was empty if one of XX or YY is empty, i.e. ∅\varnothing is not a unit object) and added Milnor’s join construction (which has the same underlying set but the coarse topology w.r.t. the coordinate projections) to address Qayum Khan’s complaints. (I really ought to have defined infinitary joins with the colimit topology (which is a nice coend) and with Milnor’s ‘strong’ (=coarse) topology, which tom Dieck’s Algebraic topology uses to define EG=G ⋆¯ωEG = G^{\bar\star\omega} in one go; maybe next time…) I also added the definition of the fibrewise (Milnor) join of spaces, and its role in Strøm’s construction of the (cofibration, acyclic fibration)-factorization in the h-model structure.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2022

    I am pasting it in, let’s see if it works for me…

    diff, v11, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2022
    • (edited May 6th 2022)

    Seems to have worked. Please check if your edits are there as intended.

    Sometimes strings inside unusual author names or the like trigger the spam filter (eg “Tangora” was once rejected, for including “Tango” :-)

    but otherwise it seems to reject edits that it considers suspiciously voluminous. In this case one can work around it by submitting smaller bits of new material at a time

    (I believe me and other regulars have been exempt from this, which may be the reason why I could submit your material.)

    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 6th 2022

    I believe the pushout description is correct (e.g., if XX is empty, then the construction boils down to YY); was there something else that was meant by quotient space construction?

    • CommentRowNumber6.
    • CommentAuthorTodd_Trimble
    • CommentTimeMay 6th 2022

    Oh, I see, we have the editing history back. I see it now.

    • CommentRowNumber7.
    • CommentAuthorGuest
    • CommentTimeMay 6th 2022
    Oh dear, it seems my edits were added in twice, \mathbin{\bar\star} is not valid iTex (maybe \circ was better after all…), and I forgot to add references called #Hall1956 and #Lemmens1970 (those should be

    * {#Hall1956} I.M. Hall, _The generalized Whitney sum_, The Quarterly Journal of Mathematics 16(4): 360–384, December 1965. [10.1093/qmath/16.4.360](https://doi.org/10.1093/qmath/16.4.360)

    * {#Lemmens1970} P.W.H. Lemmens, _A note on the join of fibrations_, Indagationes Mathematicae 73: 53–56 (1970) [doi:10.1016/S1385-7258(70)80008-7](https://doi.org/10.1016/S1385-7258(70)80008-7)

    respectively). Sorry for the mess…
    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2022

    Oh, I see. Sorry, I was doing this from my phone. Let me get to my laptop and salvage this….

    • CommentRowNumber9.
    • CommentAuthorGuest
    • CommentTimeMay 6th 2022
    Here’s a fixed edit (with \circ instead of \mathbin{\bar\star} and the missing references restored): https://pastebin.com/raw/HfFA0L0r

    (It’s a link to the raw paste data, which it contains only once)
    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2022

    Okay thanks. Second attempt now. Please check.

    diff, v12, current

    • CommentRowNumber11.
    • CommentAuthorGuest
    • CommentTimeMay 6th 2022
    Rather mysteriously, the two “\bar \star”’s (with space!) apparently _are_ valid iTeX, so here is a version with \mathbin{\bar \star} instead of \circ (following Fritsch–Golasiński’s notation): https://pastebin.com/raw/2b84tB3Y
    • CommentRowNumber12.
    • CommentAuthorGuest
    • CommentTimeMay 6th 2022

    Oh, I was posting during #10. Looks no worse than what I wrote 😅

    • CommentRowNumber13.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2022

    Pasted in once more. But have you tried if you can make edits in the latest version?.

    I’ll be offline for tonight.

    diff, v12, current

    • CommentRowNumber14.
    • CommentAuthorUrs
    • CommentTimeMay 6th 2022

    Maybe what you want is “⋆¯\overline{\star}”? Try this:

      \overline{\star}
    • CommentRowNumber15.
    • CommentAuthorGuest
    • CommentTimeMay 6th 2022

    Ah yes, \overline{\star} looks good (without the \mathbin{}, with which it isn’t even valid iTeX…). The references are fixed, spam filter placated, \stars \overlined, i’s crossed and t’s dotted. Thanks for the help, and goodnight!

1 to 15 of 15

  1.