Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 60, No. 2, pp. 139-160 (2003)

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The Convergence Approach to Exponentiable Maps

Maria Manuel Clementino, Dirk Hofmann and Walter Tholen

Departamento de Matemática, Universidade de Coimbra,
Apartado 3008, 3001-454 Coimbra -- PORTUGAL
E-mail: mmc@mat.uc.pt , dirk@mat.uc.pt
Department of Mathematics and Statistics, York University,
Toronto, CANADA M3J 1P3 -- CANADA
E-mail: tholen@mathstat.yorku.ca

Abstract: Exponentiable maps in the category $\Top$ of topological spaces are characterized by an easy ultrafilter-interpolation property, in generalization of a recent result by Pisani for spaces. From this characterization we deduce that perfect (= proper and separated) maps are exponentiable, generalizing the classical result for compact Hausdorff spaces. Furthermore, in generalization of the Whitehead--Michael characterization of locally compact Hausdorff spaces, we characterize exponentiable maps of $\Top$ between Hausdorff spaces as restrictions of perfect maps to open subspaces.

Keywords: exponentiable map; proper map; separated map; perfect map; partial product; ultrarelational structure; grizzly space; pseudo-topological space.

Classification (MSC2000): 54C10, 54C35, 54B30, 18D15.

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Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.

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