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... if for each pair of distinct fuzzy points xε and yν in X, there exist disjoint fuzzy clopen sets β and µ in X such that xε ∈ β and yν ∈ µ. Theorem 20. If f : X → Y is a fuzzy slightly precontinuous injection and Y is fuzzy co-T2 , then X is fuzzy p-T2 . Proof. For any pair of distict fuzzy points xε ...

... if for each pair of distinct fuzzy points xε and yν in X, there exist disjoint fuzzy clopen sets β and µ in X such that xε ∈ β and yν ∈ µ. Theorem 20. If f : X → Y is a fuzzy slightly precontinuous injection and Y is fuzzy co-T2 , then X is fuzzy p-T2 . Proof. For any pair of distict fuzzy points xε ...

Fuzzy Proper Mapping

... The concept of fuzzy sets and fuzzy set operation were first introduced by ( L. A. Zadeh ). Several other authors applied fuzzy sets to various branches of mathematics . One of these objects is a topological space .At the first time in 1968 , (C .L. Chang) introduced and developed the concept of fuz ...

... The concept of fuzzy sets and fuzzy set operation were first introduced by ( L. A. Zadeh ). Several other authors applied fuzzy sets to various branches of mathematics . One of these objects is a topological space .At the first time in 1968 , (C .L. Chang) introduced and developed the concept of fuz ...

... are denoted by 0 x ,1x , respectively. A fuzzy set is said to be quasi- coincident with a fuzzy set , denoted by q , if there exists x X such that (x)+(x)>1[8]. Obviously, for any two fuzzy set and , q will simply q . A fuzzy set in a fts (X,) is called a q-nbd of a fuzzy point ...

CW-complexes in the category of exterior spaces

... developing a theory of exterior CW-complexes. This study will give several interesting consequences in proper homotopy. Among these results we can mention Proper Whitehead Theorem Proper Cellular Approximation Theorem (they may also be proved within the proper setting) The Proper Blackers-Massey The ...

... developing a theory of exterior CW-complexes. This study will give several interesting consequences in proper homotopy. Among these results we can mention Proper Whitehead Theorem Proper Cellular Approximation Theorem (they may also be proved within the proper setting) The Proper Blackers-Massey The ...

Fuzzy Strongly Locally Connected Space By Hanan Ali

... separation axioms are assumed unless explicitly stated .For a fuzzy set A in X , A and A denote the fuzzy interior and fuzzy closure of A respectively . By 0 X and 1 X we will mean the fuzzy sets with constant function 0 ( Zero function ) and 1 ( Unit function ) respectively. This paper includes thr ...

... separation axioms are assumed unless explicitly stated .For a fuzzy set A in X , A and A denote the fuzzy interior and fuzzy closure of A respectively . By 0 X and 1 X we will mean the fuzzy sets with constant function 0 ( Zero function ) and 1 ( Unit function ) respectively. This paper includes thr ...

Fuzzy Regular Compact Space

... Remark 2.20. Every fuzzy regular open set is a fuzzy open set and every fuzzy regular closed set is a fuzzy closed set . The converse of remark ( 2.20 ) , is not true in general as the following example shows : Example 2.21. Let be a set and be a fuzzy topology on . Notice that is a fuzzy open set i ...

... Remark 2.20. Every fuzzy regular open set is a fuzzy open set and every fuzzy regular closed set is a fuzzy closed set . The converse of remark ( 2.20 ) , is not true in general as the following example shows : Example 2.21. Let be a set and be a fuzzy topology on . Notice that is a fuzzy open set i ...

ON PRE-I-OPEN SETS, SEMI-I-OPEN SETS AND bI

... [13] of K with respect to τ and I is defined as follows: for K ⊂ X, K ∗ (I, τ ) = {x ∈ X : U ∩K ∈ / I for every U ∈ τ (x)} where τ (x) = {U ∈ τ : x ∈ U }. A Kuratowski closure operator Cl∗ (.) for a topology τ ∗ (I, τ ), called the ?-topology, finer than τ , is defined by Cl∗ (K) = K ∪ K ∗ (I, τ ) [ ...

... [13] of K with respect to τ and I is defined as follows: for K ⊂ X, K ∗ (I, τ ) = {x ∈ X : U ∩K ∈ / I for every U ∈ τ (x)} where τ (x) = {U ∈ τ : x ∈ U }. A Kuratowski closure operator Cl∗ (.) for a topology τ ∗ (I, τ ), called the ?-topology, finer than τ , is defined by Cl∗ (K) = K ∪ K ∗ (I, τ ) [ ...

Topolog´ıa Algebraica de Espacios Topológicos Finitos y Aplicaciones

... between simple homotopy types of finite spaces and of simplicial complexes. This fundamental result allows us to study well-known geometrical problems from a new point of view, using all the combinatorial and topological machinery proper of finite spaces. Quillen’s conjecture on the poset of p-subgr ...

... between simple homotopy types of finite spaces and of simplicial complexes. This fundamental result allows us to study well-known geometrical problems from a new point of view, using all the combinatorial and topological machinery proper of finite spaces. Quillen’s conjecture on the poset of p-subgr ...