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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

... Definition2.7: A crisp subset B of a fuzzy topological space (X,) is said to be fuzzy w-compact if B is fuzzy w-compact as a fuzzy subspace of X. Theorem2.10: A fuzzy w-closed crisp subset of a fuzzy w-compact space is fuzzy w-compact relative to X. Proof: Let A be a fuzzy w-closed crisp set of fuz ...
On Fuzzy δ-I-Open Sets and Decomposition of Fuzzy α-I
On Fuzzy δ-I-Open Sets and Decomposition of Fuzzy α-I

... for some x∈X will be denoted by A(x). For any two fuzzy sets A and B in (X,τ), A≤B if and only if A(x)≤B(x) for each x∈X. A fuzzy set in (X,τ) is said to be quasi-coincident with a fuzzy set B, denoted by AqB, if there exists x∈X such that A(x) + B(x) >1 [16]. A fuzzy set V in (X,τ) is called a q-ne ...
Totally Somewhat Fuzzy Continuous and Totally Somewhat Fuzzy
Totally Somewhat Fuzzy Continuous and Totally Somewhat Fuzzy

UTILIZING SUPRA α-OPEN SETS TO
UTILIZING SUPRA α-OPEN SETS TO

... In 1965, Njastad [13] presented and investigated a notion of α-open sets in topological spaces. Mildly compact (Mildly Lindelöf) spaces [15] were introduced in 1974 and almost compact spaces [9] were introduced in 1975 by Staum and Lambrinos, respectively. Mashhour et al.[11] introduced a concept o ...
Gδ–SEPARATION AXIOMS IN ORDERED FUZZY TOPOLOGICAL
Gδ–SEPARATION AXIOMS IN ORDERED FUZZY TOPOLOGICAL

... Definition 3. A fuzzy set µ is a fuzzy topological space (X, T ) is called a fuzzy Gδ -neighbourhood of x ∈ X if there exists a fuzzy Gδ -set µ1 with µ1 ≤ µ and µ1 (x) = µ(x) > 0. It is easy to see that a fuzzy set is fuzzy Gδ - if and only if µ is a fuzzy Gδ neighbourhood of each x ∈ X for which µ( ...
Fuzzy rw-Connectedness and Fuzzy rw
Fuzzy rw-Connectedness and Fuzzy rw

Closed and closed set in supra Topological Spaces
Closed and closed set in supra Topological Spaces

Some types of fuzzy open sets in fuzzy topological groups
Some types of fuzzy open sets in fuzzy topological groups

... C.L.CHANG, Fuzzy topological spaces, 45, 182-190 (1968). A. ROSENFELD, Fuzzy groups, Journal of Mathematical Analyses and Applications. 35, 512-517 (1971). B. HUTTON, Normality in Fuzzy Topological Spaces, Journal of Mathematical Analyses and Applications. 50, 74-79 (1975). R. LOWEN, Fuzzy Topologic ...
FUZZY r-REGULAR OPEN SETS AND FUZZY ALMOST r
FUZZY r-REGULAR OPEN SETS AND FUZZY ALMOST r

Fuzzy Strongly Locally Connected Space By Hanan Ali
Fuzzy Strongly Locally Connected Space By Hanan Ali

on fuzzy ˛-continuous multifunctions
on fuzzy ˛-continuous multifunctions

GENERALISED FUZZY CONTINUOUS MAPS IN FUZZY TOPOLOGICAL SPACES Author: Ravi Pandurangan
GENERALISED FUZZY CONTINUOUS MAPS IN FUZZY TOPOLOGICAL SPACES Author: Ravi Pandurangan

b − I-OPEN SETS AND DECOMPOSITION OF CONTINUITY VIA
b − I-OPEN SETS AND DECOMPOSITION OF CONTINUITY VIA

... sets which is weaker than that of I-open sets. At last Hatir at all [5] have introduced the notions of BI -sets, CI -sets, α − I-sets, semi-I-sets and β − I-sets. By using this sets, they provided decompositions of continuity. In this paper, we introduced the notions b − I-open and strong BI -sets t ...
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 ) [ ...
CHARACTERIZATIONS OF FUZZY α
CHARACTERIZATIONS OF FUZZY α

Fuzzy Irg- Continuous Mappings
Fuzzy Irg- Continuous Mappings

View PDF - Journal of Computer and Mathematical Sciences
View PDF - Journal of Computer and Mathematical Sciences

Soft separation axioms in soft topological spaces
Soft separation axioms in soft topological spaces

... and theory of measurement. Maji et. al [20] applied soft sets in a multicriteria decision making problems. It is based on the notion of knowledge reduction of rough sets. They applied the technique of knowledge reduction to the information table induced by the soft set. In [21], they defined and stu ...
A STUDY ON FUZZY LOCALLY δ- CLOSED SETS
A STUDY ON FUZZY LOCALLY δ- CLOSED SETS

this PDF file - International Journal of Mathematical Archive
this PDF file - International Journal of Mathematical Archive

... The fuzzy set A is fuzzy-supper closed if A+ = A and fuzzy supper open if A−=A. A is fuzzy supper-open if and only if A is fuzzy supper-closed. Definition 3.2: A mapping f: X → Y from a fuzzy topological space (X, δ1) to a fuzzy topological space (Y, δ2) is said to be fuzzy supper-continuous if the ...
ON FUZZY NEARLY C-COMPACTNESS IN FUZZY TOPOLOGICAL
ON FUZZY NEARLY C-COMPACTNESS IN FUZZY TOPOLOGICAL

Soft ̃ Semi Open Sets in Soft Topological Spaces
Soft ̃ Semi Open Sets in Soft Topological Spaces

Fuzzy g**- Closed Sets
Fuzzy g**- Closed Sets

On Fuzzy γ - Semi Open Sets and Fuzzy γ - Semi
On Fuzzy γ - Semi Open Sets and Fuzzy γ - Semi

1 2 3 4 5 ... 66 >

Sheaf (mathematics)

In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space. The data can be restricted to smaller open sets, and the data assigned to an open set is equivalent to all collections of compatible data assigned to collections of smaller open sets covering the original one. For example, such data can consist of the rings of continuous or smooth real-valued functions defined on each open set. Sheaves are by design quite general and abstract objects, and their correct definition is rather technical. They exist in several varieties such as sheaves of sets or sheaves of rings, depending on the type of data assigned to open sets.There are also maps (or morphisms) from one sheaf to another; sheaves (of a specific type, such as sheaves of abelian groups) with their morphisms on a fixed topological space form a category. On the other hand, to each continuous map there is associated both a direct image functor, taking sheaves and their morphisms on the domain to sheaves and morphisms on the codomain, and an inverse image functor operating in the opposite direction. These functors, and certain variants of them, are essential parts of sheaf theory.Due to their general nature and versatility, sheaves have several applications in topology and especially in algebraic and differential geometry. First, geometric structures such as that of a differentiable manifold or a scheme can be expressed in terms of a sheaf of rings on the space. In such contexts several geometric constructions such as vector bundles or divisors are naturally specified in terms of sheaves. Second, sheaves provide the framework for a very general cohomology theory, which encompasses also the ""usual"" topological cohomology theories such as singular cohomology. Especially in algebraic geometry and the theory of complex manifolds, sheaf cohomology provides a powerful link between topological and geometric properties of spaces. Sheaves also provide the basis for the theory of D-modules, which provide applications to the theory of differential equations. In addition, generalisations of sheaves to more general settings than topological spaces, such as Grothendieck topology, have provided applications to mathematical logic and number theory.
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