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ON FUZZY ALMOST CONTRA γ-CONTINUOUS FUNCTIONS K
ON FUZZY ALMOST CONTRA γ-CONTINUOUS FUNCTIONS K

Properties of Pre- -Open Sets and Mappings
Properties of Pre- -Open Sets and Mappings

PDF
PDF

... 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 ...
On the forms of continuity for fuzzy functions
On the forms of continuity for fuzzy functions

Fuzzy Proper Mapping
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 ...
SOME STRONGER FORMS OF FUZZY CONTINOUS MAPPINGS 1
SOME STRONGER FORMS OF FUZZY CONTINOUS MAPPINGS 1

FUZZY SEMI α-IRRESOLUTE FUNCTIONS 1. Introduction The fuzzy
FUZZY SEMI α-IRRESOLUTE FUNCTIONS 1. Introduction The fuzzy

view full paper - International Journal of Scientific and Research
view full paper - International Journal of Scientific and Research

on fuzzy weakly semiopen functions
on fuzzy weakly semiopen functions

ON Compactly fuzzy
ON Compactly fuzzy

Fuzzy rw-Connectedness and Fuzzy rw
Fuzzy rw-Connectedness and Fuzzy rw



... 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 ...
Totally Somewhat Fuzzy Continuous and Totally Somewhat Fuzzy
Totally Somewhat Fuzzy Continuous and Totally Somewhat Fuzzy

Gδ–SEPARATION AXIOMS IN ORDERED FUZZY TOPOLOGICAL
Gδ–SEPARATION AXIOMS IN ORDERED FUZZY TOPOLOGICAL

CW-complexes in the category of exterior spaces
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 ...
On Fuzzy Maximal θ-Continuous Functions in Fuzzy Topological
On Fuzzy Maximal θ-Continuous Functions in Fuzzy Topological

Some kinds of fuzzy connected and fuzzy continuous functions
Some kinds of fuzzy connected and fuzzy continuous functions

Fuzzy Strongly Locally Connected Space By Hanan Ali
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 ...
UTILIZING SUPRA α-OPEN SETS TO
UTILIZING SUPRA α-OPEN SETS TO

Fuzzy Regular Compact Space
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
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
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 ...
More Functions Associated with Semi-Star-Open Sets
More Functions Associated with Semi-Star-Open Sets

CHARACTERIZATIONS OF FUZZY α
CHARACTERIZATIONS OF FUZZY α

On Fuzzy δ-I-Open Sets and Decomposition of Fuzzy α-I
On Fuzzy δ-I-Open Sets and Decomposition of Fuzzy α-I

1 2 3 4 5 ... 106 >

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.
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