Fuzzy weakly completely continuous functions
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Cites background from "Fuzzy weakly completely continuous ..."
...For definitions and results not explained in this paper, the reader is referred a [1,3,6,7,10,11,13] assuming them to be well known....
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Additional excerpts
...Recall that, a function f : (X, τ1) → (Y, τ2) is said to be fuzzy strongly continuous [2], if for every fuzzy subset λ of X, f(Cl(λ)) ≤ f(λ)....
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...[2] Let λ be a fuzzy set in a fts X, then: 1) λ is a fuzzy θ-open if and only if λ = Intθ(λ)....
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Additional excerpts
...The mapping f is called: 1) fuzzy continuous if f (1)(B) 2 1, for each B 2 2 [6]; 2) fuzzy weakly continuous if f (1)(B) 6 int f (1)(clB), for each B 2 2 [1]; 3) fuzzy strongly precontinuous if f (1)(B) 2 FSPO( 1), for each B 2 2 [8]; 4) fuzzy irresolute continuous if f (1)(B) 2 FSO( 1), for eachB 2 FSO( 2) [13]; 5) fuzzy preirresolute continuous if f (1)(B) 2 FPO( 1), for each B 2 FPO( 2) [7]; 6) fuzzy strongly irresolute continuous if f (1)(B) 2 FSSO( 1), for each B 2 FSSO( 2) [2]; 7) fuzzy R-continuous if f (1)(B) 2 FRO( 1), for each B 2 FRO( 2) [3]; 8) fuzzy open (closed) if f(A) 2 2 (f(A) c 2 2), for each A 2 1 (A c 2 1) [12]; 9) fuzzy strongly preopen (preclosed) if f(A) 2 FSPO( 2) (f(A) 2 FSPC( 2)), for each A 2 1 (A c 1) [8]; 10) fuzzy irresolute open (closed) if f(A) 2 FSO( 2) (f(A) 2 FSC( 2)), for each A 2 FSO( 1) (A 2 FSC( 1)) [13]; 11) fuzzy preirresolute open (closed) if f(A) 2 FPO( 2) (f(A) 2 FPC( 2)), for each A 2 FPO( 1) (A 2 FPC( 1)) [7]; 12) fuzzy strongly irresolute open (closed) if f(A) 2 FSSO( 2) (f(A) 2 FSSC( 2)), for each A 2 FSSO( 1) (A 2 FSSC( 1)) [2]; 13) fuzzy R-open (R-closed) if f(A) 2 FRO( 2) (f(A) 2 FRC( 2)), for each A 2 FRO( 1) (A 2 FRC( 1)) [3]; 14) fuzzy homeomorphism if it is bijective and f and f 1 are fuzzy continuous [6]....
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Cites background or methods from "Fuzzy weakly completely continuous ..."
...In this paper, we introduce the concepts of fuzzy completely Ak-continuous functions (where Ak is an operations on I x of a fuzzy topological space X) as a generalizations of a class of fuzzy complete continuity such as fuzzy complete continuity rio], fuzzy completely irresolute [4], fuzzy weak completely irresolute 1-4] and fuzzy weak complete continuity [2]....
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...fuzzy completely irresolute [4], fuzzy weak completely irresolute [4], fuzzy weak completely continuous [-2], fuzzy R-Map [2]) iff f - I ( B ) is a fuzzy regular open set of X for each fuzzy open (resp....
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...Then f is called fuzzy completely continuous [3] (resp. fuzzy completely irresolute [4], fuzzy weak completely irresolute [4], fuzzy weak completely continuous [-2], fuzzy R-Map [2]) iff f -...
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...(c) In [2] Example 5 shows that fuzzy R-Map is not FC-cont function and thus fuzzy R-Map is not FCfl-cont function....
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...As a corollary of Theorem 3.7 above and by considering all the function studied here, we have the following mutual relationships: FCS-cont FR-Map FCfl-cont FCct-cont --....
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References
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