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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 ...
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 ...
... 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 ...
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 ...
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 ...
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 ) [ ...
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 ...
Grothendieck topology
In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space. A category together with a choice of Grothendieck topology is called a site.Grothendieck topologies axiomatize the notion of an open cover. Using the notion of covering provided by a Grothendieck topology, it becomes possible to define sheaves on a category and their cohomology. This was first done in algebraic geometry and algebraic number theory by Alexander Grothendieck to define the étale cohomology of a scheme. It has been used to define other cohomology theories since then, such as l-adic cohomology, flat cohomology, and crystalline cohomology. While Grothendieck topologies are most often used to define cohomology theories, they have found other applications as well, such as to John Tate's theory of rigid analytic geometry.There is a natural way to associate a site to an ordinary topological space, and Grothendieck's theory is loosely regarded as a generalization of classical topology. Under meager point-set hypotheses, namely sobriety, this is completely accurate—it is possible to recover a sober space from its associated site. However simple examples such as the indiscrete topological space show that not all topological spaces can be expressed using Grothendieck topologies. Conversely, there are Grothendieck topologies which do not come from topological spaces.