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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJan 5th 2014
   • PermaLink
   Author: Urs
   Format: MarkdownItexat _[[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.

   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.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 14th 2020
   • (edited Dec 14th 2020)
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   Author: Urs
   Format: MarkdownItexAdded the statement that on the [[subcategory]] $Top_{LCHaus}$ of [[Top]] on the [[locally compact Hausdorff spaces]] with [[proper maps]] between them, the [[functor]] of [[one-point compactification]] $$ (-)^{cpt} \;\colon\; Top_{LCHaus} \longrightarrow Top^{\ast/} $$ sends [[Cartesian products]] ([[product topological spaces]]) to [[smash products]] of [[pointed topological spaces]], in that there is a [[natural transformation|natural]] [[homeomorphism]]: $$ \big( X \times Y \big)^{cpt} \;\simeq\; X^{cpt} \wedge Y^{cpt} \,. $$ 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]]_). <a href="https://ncatlab.org/nlab/revision/diff/smash+product/21">diff</a>, <a href="https://ncatlab.org/nlab/revision/smash+product/21">v21</a>, <a href="https://ncatlab.org/nlab/show/smash+product">current</a>

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

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

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

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

   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