Algebra, Logic and Topology

 

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details

Author(s)
Dirk Hofmann; Maria Manuel Clementino; Walter Tholen;

Title
The convergence approach to exponentiable maps

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.

Journal
Portugaliae Mathematica

Volume
60

Year
2003

Issue

Page(s)
139-160

 
     
 

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