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nLab > Latest Changes: join of topological spaces

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  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

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