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Right adjoint for the smash product functor


Author: Francesca Cagliari
Journal: Proc. Amer. Math. Soc. 124 (1996), 1265-1269
MSC (1991): Primary 54B30; Secondary 18A40
DOI: https://doi.org/10.1090/S0002-9939-96-03065-1
MathSciNet review: 1301490
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Abstract: The smash-product functor $(\text{--})\wedge{(X,x_0)}$ 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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Additional Information

Francesca Cagliari
Affiliation: Dipartimento di Matematica, Piazza di Porta San Donato, 5, 40127 Bologna, Italy
Email: cagliari@dm.unibo.it

DOI: https://doi.org/10.1090/S0002-9939-96-03065-1
Received by editor(s): November 3, 1993
Received by editor(s) in revised form: August 19, 1994
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1996 American Mathematical Society

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