International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 12, Pages 737-748
Fuzzy properties in fuzzy convergence spaces
Department of Mathematics (Pure and Applied), Rhodes University, Grahamstown 6140, South Africa
Received 10 March 2001; Revised 20 May 2001
Copyright © 2002 Gunther Jäger. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Based on the concept of limit of prefilters and residual
implication, several notions in fuzzy topology are fuzzyfied in
the sense that, for each notion, the degree to which it is
fulfilled is considered. We establish therefore theories of
degrees of compactness and relative compactness, of closedness,
and of continuity. The resulting theory generalizes the
corresponding crisp theory in the realm of fuzzy convergence
spaces and fuzzy topology.