Inverse limits in the category of compact Hausdorff spaces and upper semicontinuous functions

Authors

  • I. Banic University of Maribor
  • T. Sovic University of Maribor

Keywords:

Upper semi-continuous functions, Inverse limits, Weak inverse limits

Abstract

We investigate inverse limits in the category \(\mathcal{CHU}\) of compact Hausdorff spaces with upper semicontinuous functions. We introduce the notion of weak inverse limits in this category and show that the inverse limits with upper semicontinuous set-valued bonding functions (as they were defined by Ingram and Mahavier [‘Inverse limits of upper semi-continuous set valued functions’, Houston J. Math. 32 (2006), 119–130]) together with the projections are not necessarily inverse limits in \(\mathcal{CHU}\) but they are always weak inverse limits in this category. This is a realisation of our categorical approach to solving a problem stated by Ingram [An Introduction to Inverse Limits with Set-Valued Functions (Springer, New York, 2012)]. 10.1017/S0004972713000245

Published

2013-12-02

Issue

Vol. 89 No. 1 (2014)

Section

Articles
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