Stable subconstructs of FTS: Part II

Löwen, R.; Wuyts, P.

doi:10.1016/0165-0114(95)00055-p

Cited by 20 publications

(16 citation statements)

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“…The importance of the existence of nontrivial both initially and finally full subconstructs of L-FTS lies in that, as observed by Lowen and Wuyts [24], each such subconstruct of FTS gives rise to a perfectly viable and natural autonomous theory of fuzzy topology." Putting this differently, fuzzy topology should consist of a system of closely related theories of topology, each such theory applying to a subuniverse of L-FTS.…”

Section: Let Have a Base Consisting Of Elements Preserving Nonempty Fmentioning

confidence: 95%

“…In the case L = 0 1 , Lowen and Wuyts [23,24] proved that L-FTS contains many such subconstructs, and a nice characterization and classification theorem of these subconstructs was also presented in their papers. For a general completely distributive lattice L, L-FTS also has nontrivial both initially and finally closed full subconstructs other than ω L Top ; for example, the construct of Lowen spaces in [18] is one of such subconstruct.…”

Section: Lowen Functors and Subuniverses Of L-ftsmentioning

confidence: 95%

“…Then easily L is a total L-fuzzy topology on L. Moreover, L = ω L S where S denotes the Scott topology on L. It is easy to check that ω L Top =Stab( L [19,23].…”

Section: Lowen Functors and Subuniverses Of L-ftsmentioning

confidence: 98%

“…Let N be the L-fuzzy topology on L generated by σ ∈ L σ ≤ id L ∪ constants , then N is a total L-fuzzy topology on L and Stab N is the construct of Lowen spaces [18]. Particularly when L = 0 1 , Stab N ) is the construct FNS of fuzzy neighbourhood spaces [23].…”

Section: Lowen Functors and Subuniverses Of L-ftsmentioning

confidence: 98%

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Some Categorical Aspects of Fuzzy Topology

Liu

Zhang

Luo

2000

Journal of Mathematical Analysis and Applications

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Research in recent years has revealed that the construct of fuzzy topological spaces behaves quite differently from that of topological spaces with respect to certain categorical properties. In this paper we discuss some of these aspects. Since the topological construct L-FTS contains nontrivial both initially and finally closed full subconstructs, and each such construct gives rise to a natural autonomous theory of fuzzy topology, it can be said to some extent that fuzzy topology should consist of a system of closely related topology theories, including the classical topology theory as a special case, with each applying to one such subconstruct. Therefore in the first part of this paper the theory of sobriety is established for each finally and initially closed full subconstruct of L-FTS to illustrate this idea. The second topic of this paper is the relationship between the construct of stratified L-fuzzy topological spaces and several other familiar constructs in fuzzy topology, for example, the constructs ofSostak fuzzy topological spaces and L-fuzzifying topological spaces. © 2000 Academic PressKey Words: fuzzy topology; sobriety; frame; topological construct; co-tower extension; total fuzzy topology. PRELIMINARIESAfter a development period of more than 30 years, fuzzy topology has become rather diverse in its topics as well as its methods. The recent book [17] is a comprehensive treatment of the general topology and lattice theoretic aspects of fuzzy topology. In this paper we deal with some categorical properties of the construct of fuzzy topological spaces.

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Section: Let Have a Base Consisting Of Elements Preserving Nonempty Fmentioning

confidence: 95%

Section: Lowen Functors and Subuniverses Of L-ftsmentioning

confidence: 95%

“…Then easily L is a total L-fuzzy topology on L. Moreover, L = ω L S where S denotes the Scott topology on L. It is easy to check that ω L Top =Stab( L [19,23].…”

Section: Lowen Functors and Subuniverses Of L-ftsmentioning

confidence: 98%

Section: Lowen Functors and Subuniverses Of L-ftsmentioning

confidence: 98%

See 2 more Smart Citations

Some Categorical Aspects of Fuzzy Topology

Liu

Zhang

Luo

2000

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…Since this is true for any increasing homeomorphism on the unit interval, it is natural to look at fuzzy topologies which are invariant under such operations, in the sense that for any increasing homeomorphism cp : I + I, cp o A c A, and to try and discover precisely what these fuzzy topologies look like. The techniques developed in [3] and [12] are perfectly suited for this purpose. In this paper we then also describe the total fuzzy topology generated by the set of all increasing homeomorphisms on the unit interval, and derive a characterization of the, hence simultaneously bireflective and bicoreflective, subconstruct of FTS consisting of objects with fuzzy topologies stable under increasing homeomorphisms in the above sense.…”

Section: Introductionmentioning

confidence: 99%