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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 26th 2021
    • (edited Jan 26th 2021)

    We had (still have) a proof of the contractibility of some version of S S^\infty in the Definition-section at n-sphere.

    Since that doesn’t seem to be the right place for that material, and in order to make it easier to link to S S^\infty and its contractibility, I am giving it its own page here.

    In creating this page, I have:

    • copied over the material of the section n-sphere – Definition – Infinite-dimensional sphere;

    • expanded out the first paragraph into a new Idea-section here;

    • added a section with the definition as a colimit over relative cell complex inclusions and the quick proof of weak contractibility from that.

    So the previous discussion in terms of infinite-dimensional unit spheres in LCTVSs and/or in shift spaces is currently both here as well as inside n-sphere. But I suggest we remove it at the latter place, and just leave the link to this new page here.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorTodd_Trimble
    • CommentTimeJan 26th 2021

    Something I wondered about reading this page is whether the topology coming from the l 2l^2 norm coincides with the coherent/colimit topology. I am told this follows from something called the Banach-Dieudonne theorem. Does anyone have more information on this?