Neighborhoods, bases and continuity in fuzzy topological spaces
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This article is published in Rocky Mountain Journal of Mathematics.The article was published on 1978-09-01 and is currently open access. It has received 124 citations till now. The article focuses on the topics: Topological space & Topological vector space.read more
Citations
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Book ChapterDOI
Axiomatic Foundations Of Fixed-Basis Fuzzy Topology
Ulrich Höhle,Alexander P. Sostak +1 more
TL;DR: This paper gives the first comprehensive account on various systems of axioms of fixed-basis, L-fuzzy topological spaces and their corresponding convergence theory.
Journal ArticleDOI
Fuzzy topological vector spaces II
TL;DR: The notion of a bornological fuzzy linear space is given and some of the properties of such a space are investigated.
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A Comparison of Different Compactness Notions in Fuzzy Topological Spaces
TL;DR: In this paper, the authors studied the different kinds of compactness notions that have been introduced up to this time and studied the implications that exist between the different notions, and in Section 5 they gave some concluding remarks.
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Compactness in fuzzy topological spaces
TL;DR: It is observed that it is possible to have degrees of compactness, which is called α-compactness (α a member of a designated lattice), and a Tychonoff Theorem is obtained for an arbitrary product of α-Compact fuzzy spaces and a 1-point compactification.
References
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Journal ArticleDOI
Fuzzy topological spaces and fuzzy compactness
TL;DR: It will be shown in a following publication that contrary to the results obtained up to now, the Tychonoff-product theorem is safeguarded with fuzzy compactness.
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Normality in fuzzy topological spaces
TL;DR: In this article, the notion of normality in topological spaces is extended to fuzzy topologies, and a fuzzy topological space is constructed in terms of a Urysohn type lemma.
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The fuzzy tychonoff theorem
TL;DR: In this article, the authors define cl∞-monoids, which are used to measure the degree of membership of points in sets, and define L- or "fuzzy" sets are defined, and suitable collections of these are called L-topological spaces.
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Fixed points, separation, and induced topologies for fuzzy sets
TL;DR: This paper considers how a topology for a set 3 may give rise to an “induced fuzzy topology” for S, thus characterizing the fuzzy subsets of % which may naturally be considered “open” and furnishing a concrete class of examples of the “fuzzy topologies” defined by C. L. Chang.