Fuzzy connectedness and its stronger forms. (English) Zbl 0588.54008

Fatteh, U. V.; Bassan, D. S.

J. Math. Anal. Appl. 111, 449-464 (1985).

A topological space is said to be superconnected if each nonempty open subset is dense, and strongly connected if it is not the union of two nonempty proper open subsets. The authors study the analogues of ordinary connectedness and these two strong forms of connectedness in fuzzy topological spaces. Many elementary theorems on connectedness hold in the setting of fuzzy spaces, but some do not. For example, the fuzzy product of fuzzy connected spaces need not be fuzzy connected. The paper contains a very nice introduction to fuzzy sets and fuzzy topological spaces.

Reviewer: B.J.Pearson

MSC:

54A40	Fuzzy topology
54D05	Connected and locally connected spaces (general aspects)

Keywords:

fuzzy connectedness; superconnectedness; strong forms of connectedness

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