Connectedness and local connectedness in Lowen spaces

Authors:
Sheng-Gang Li
Affiliations:
College of Mathematics and Information Science, Shaanxi Normal University, 710062 Xi'an, PR China
Venue:
Fuzzy Sets and Systems
Year:
2007

Citing 8
Cited 1

Connectedness on fuzzy topological spaces

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On fuzzy connectedness

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Abstract and concrete categories

Abstract and concrete categories
Induced I(L)-fuzzy topological spaces

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On the sum of L-fuzzy topological spaces

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Connectedness in L-fuzzy topological spaces

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Local connectedness in L-topological spaces

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Higher separation axioms in L-topologically generated I(L)-topological spaces

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Lowen LM-fuzzy topological spaces

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Abstract

A fuzzy connectedness axiom and a matching fuzzy local connectedness are defined in this paper for Lowen spaces. It is shown that such Lowen spaces have properties corresponding to those of traditional connected and locally connected topological spaces. It is also proved that an L-topological space (X,@d) is fuzzy connected (resp., fuzzy locally connected) in our sense if and only if its induced I(L)-topological space (X,@w(@d)) is too. Some related categorical results are also obtained, and a fuzzy version of topological intersection theorems is given by using our notion of connectedness.