Fuzzy convergence: open and proper maps

Authors:
G. Richardson;Q. Xue;J. Zhang
Affiliations:
Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, FL 32816-1364, USA;Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, FL 32816-1364, USA;Department of Mathematics, University of Central Florida, P.O. Box 161364, Orlando, FL 32816-1364, USA
Venue:
Fuzzy Sets and Systems
Year:
2005

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Abstract

The notions of open and proper maps are introduced in the category FCS of fuzzy convergence spaces and each is shown to be an extension of the same notion with respect to the embedding functor from the category PCS of probabilistic convergence spaces. Proper maps in FCS are shown to be productive and, moreover, preserve closures of fuzzy sets, regularity and local precompactness. All projection maps in FCS are open and open maps are finitely productive.