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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJan 5th 2014

    at smash product I have added after the definition (for pointed sets, currently) pointers to the general discussion of the closed monoidal structure at pointed object and to the article by Elmendorf-Mandell.

    Eventually the entry smash product should be written in a bit more generality. But I won’t do it right now.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 14th 2020
    • (edited Dec 14th 2020)

    Added the statement that on the subcategory Top LCHausTop_{LCHaus} of Top on the locally compact Hausdorff spaces with proper maps between them, the functor of one-point compactification

    () cpt:Top LCHausTop */ (-)^{cpt} \;\colon\; Top_{LCHaus} \longrightarrow Top^{\ast/}

    sends Cartesian products (product topological spaces) to smash products of pointed topological spaces, in that there is a natural homeomorphism:

    (X×Y) cptX cptY cpt. \big( X \times Y \big)^{cpt} \;\simeq\; X^{cpt} \wedge Y^{cpt} \,.

    Elementary as it is, I’ll give it a little stand-alone entry one-point compactification intertwines Cartesian product with smash product for ease of hyperlinking in other relevant entries (such as at one-point compactification and pointed topological space).

    diff, v21, current

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