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“Topologically Indexed Function Spaces and Adjoint Functors”

Published online by Cambridge University Press:  20 November 2018

S. B. Niefield
S. B. Niefield*
Affiliation:
Dalhousie University, Halifax, N.S.
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Abstract

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Let Top denote the category of topological spaces and continuous maps. In this paper we discuss families of function spaces indexed by the elements of a topological space T, and their relationship to the characterization of right adjoints Top/S → Top/T, where S is also a topological space. After reducing the problem to the case where S is a one-point space, we describe a class of right adjoints Top → Top/T, and then show that every right adjoint Top → Top/T is isomorphic to one of this form. We conclude by giving necessary and sufficient conditions for a left adjoint Top/T → Top to be isomorphic to one of the form − XTY, where Y is a space over T, and xT denotes the fiber product with the product topology.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 2 , 01 June 1982 , pp. 169 - 178
Copyright
Copyright © Canadian Mathematical Society 1982

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