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The Group of L-Fuzzy Homeomorphisms and the Group of Permutations of the Ground Set

✍ Scribed by T.P. Johnson

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 70 KB
Volume: 245
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.6760

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✦ Synopsis

In this paper we study some relations between the group of L-fuzzy homeomorphisms of an L-fuzzy topological space X and the group of permutations of the ground set X. In contrast with the results in general topology, it is proved that the subgroups generated by cycles and proper normal subgroups can be represented as groups of L-fuzzy homeomorphisms for some L-fuzzy topology on X. The relation between the group of L-fuzzy homeomorphisms and the group of homeomorphisms of the associated topology is also discussed.

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