Right adjoint for the smash product functor

Cagliari, Francesca

doi:10.1090/S0002-9939-96-03065-1

Right adjoint for the smash product functor
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by Francesca Cagliari

Proc. Amer. Math. Soc. 124 (1996), 1265-1269

DOI: https://doi.org/10.1090/S0002-9939-96-03065-1

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Abstract:

The smash-product functor $(\text {–})\wedge x_0$ in the category $\underline {\mathbf {Top}}_*$ of pointed topological spaces has a right adjoint for any choice of the base point $x_0$, if and only if the topological space $X$ is quasi-locally compact, that is, if and only if the product functor $(\text {–})\times X$ has a right adjoint in the category $\underline {\mathbf {Top}}$ of topological spaces.

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