Soft filters and their convergence properties
... various uncertainties typical for those problems. In recent years, a number of theories have been proposed for dealing which such systems in an effective way. Some of these are theory of probability, theory of fuzzy sets [24], theory of intuitionistic fuzzy sets [3], theory of vague sets [10], theor ...
... various uncertainties typical for those problems. In recent years, a number of theories have been proposed for dealing which such systems in an effective way. Some of these are theory of probability, theory of fuzzy sets [24], theory of intuitionistic fuzzy sets [3], theory of vague sets [10], theor ...
CHARACTERIZATIONS OF FUZZY α
... The notations Cl(A), Int(A) and A will stand respectively for the fuzzy closure, fuzzy interior and complement of a fuzzy set A in a fts X. The support of a fuzzy set A in X will be denoted by S(A) i. e S(A) = {x ∈ X : A(x) 6= 0}. A fuzzy point xt in X is a fuzzy set having support x ∈ X and value t ...
... The notations Cl(A), Int(A) and A will stand respectively for the fuzzy closure, fuzzy interior and complement of a fuzzy set A in a fts X. The support of a fuzzy set A in X will be denoted by S(A) i. e S(A) = {x ∈ X : A(x) 6= 0}. A fuzzy point xt in X is a fuzzy set having support x ∈ X and value t ...
Closed and closed set in supra Topological Spaces
... S-S continuous functions and S* - continuous functions. In 2010, O.R.Sayed and Takashi Noiri [10] introduced supra b - open sets and supra b continuity on topological spaces. In this paper, we use closed and closed set as a tool to introduce the concept of supra supra ...
... S-S continuous functions and S* - continuous functions. In 2010, O.R.Sayed and Takashi Noiri [10] introduced supra b - open sets and supra b continuity on topological spaces. In this paper, we use closed and closed set as a tool to introduce the concept of supra supra ...
GENERALISED FUZZY CONTINUOUS MAPS IN FUZZY TOPOLOGICAL SPACES Author: Ravi Pandurangan
... Levine [9] introduced the concept of generalized closed sets of a topological space and a class of topological spaces called T1 / 2 - spaces. Dunhamm and Levine further studied some properties of generalized closed sets and T1 / 4 - spaces. Maki and Umehara studied the characterizations of T1 / 2 - ...
... Levine [9] introduced the concept of generalized closed sets of a topological space and a class of topological spaces called T1 / 2 - spaces. Dunhamm and Levine further studied some properties of generalized closed sets and T1 / 4 - spaces. Maki and Umehara studied the characterizations of T1 / 2 - ...
Chapter 1 Sheaf theory
... in the smooth case. In this chapter we provide a fairly comprehensive overview of sheaf theory. The presentation in this chapter is thorough but basic. When one delves deeply into sheaf theory, a categorical approach is significantly more efficient than the direct approach we undertake here. However ...
... in the smooth case. In this chapter we provide a fairly comprehensive overview of sheaf theory. The presentation in this chapter is thorough but basic. When one delves deeply into sheaf theory, a categorical approach is significantly more efficient than the direct approach we undertake here. However ...
IOSR Journal of Mathematics (IOSR-JM)
... Theorem4Let U be a Minimal M-g**open set.Then U = ∩ {WW is a M-g**open set of X containing x} for any element x of U. ProofBy Theorem3, and U is a Minimal M-g**open set containing x, then U W for some M-g**open set W containing x.We have U ∩ {WW is a M-g**open set of X containing x} U. Thus U ...
... Theorem4Let U be a Minimal M-g**open set.Then U = ∩ {WW is a M-g**open set of X containing x} for any element x of U. ProofBy Theorem3, and U is a Minimal M-g**open set containing x, then U W for some M-g**open set W containing x.We have U ∩ {WW is a M-g**open set of X containing x} U. Thus U ...
ON FUZZY NEARLY C-COMPACTNESS IN FUZZY TOPOLOGICAL
... 5. Fuzzy nearly C-compactness in fuzzy bitopological spaces The concept of fuzzy bitopological spaces was introduced in [5] and subsequently further studied by various authors [2], [6]. In [5] the definition of fuzzy bitopological space was given as follows: Definition 5. A fuzzy bitopological space ...
... 5. Fuzzy nearly C-compactness in fuzzy bitopological spaces The concept of fuzzy bitopological spaces was introduced in [5] and subsequently further studied by various authors [2], [6]. In [5] the definition of fuzzy bitopological space was given as follows: Definition 5. A fuzzy bitopological space ...
Surveys on Surgery Theory : Volume 1 Papers dedicated to C. T. C.
... When is a space homotopy equivalent to a finite CW complex? A space X is called finitely dominated if it is a homotopy retract of a finite CW complex K, i.e., if there exist maps f : X → K, g : K → X and a homotopy gf ' 1 : X → X. This is clearly a necessary condition for X to be of the homotopy typ ...
... When is a space homotopy equivalent to a finite CW complex? A space X is called finitely dominated if it is a homotopy retract of a finite CW complex K, i.e., if there exist maps f : X → K, g : K → X and a homotopy gf ' 1 : X → X. This is clearly a necessary condition for X to be of the homotopy typ ...
General topology
In mathematics, general topology is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology, geometric topology, and algebraic topology. Another name for general topology is point-set topology.The fundamental concepts in point-set topology are continuity, compactness, and connectedness: Continuous functions, intuitively, take nearby points to nearby points. Compact sets are those that can be covered by finitely many sets of arbitrarily small size. Connected sets are sets that cannot be divided into two pieces that are far apart. The words 'nearby', 'arbitrarily small', and 'far apart' can all be made precise by using open sets, as described below. If we change the definition of 'open set', we change what continuous functions, compact sets, and connected sets are. Each choice of definition for 'open set' is called a topology. A set with a topology is called a topological space.Metric spaces are an important class of topological spaces where distances can be assigned a number called a metric. Having a metric simplifies many proofs, and many of the most common topological spaces are metric spaces.