APPLICATIONS OF THE TARSKI–KANTOROVITCH FIXED
... Section 5 deals with the family K(X) of all nonempty compact subsets of a topological space X, endowed with the inclusion ⊇. This time the condition “b ≤ F (b)” of the T–K principle forces, in some sense, the compactness of a space, in which we work. Nevertheless, using an idea of Williams [14], we ...
... Section 5 deals with the family K(X) of all nonempty compact subsets of a topological space X, endowed with the inclusion ⊇. This time the condition “b ≤ F (b)” of the T–K principle forces, in some sense, the compactness of a space, in which we work. Nevertheless, using an idea of Williams [14], we ...
g*s-Closed Sets in Topological Spaces
... 4. g*s –continuous functions in Topological spaces Levine [ 5 ] introduced semi continuous functions using semi open sets. The study on the properties of semi-continuous functions is further carried out by Noiri[ 8 ], crossely and Hildebrand and many others. Sundram [ 13 ] introduced the concept of ...
... 4. g*s –continuous functions in Topological spaces Levine [ 5 ] introduced semi continuous functions using semi open sets. The study on the properties of semi-continuous functions is further carried out by Noiri[ 8 ], crossely and Hildebrand and many others. Sundram [ 13 ] introduced the concept of ...
this PDF file - European Journal of Pure and Applied
... Example 2. Consider X = {a, b, c} and τ = {;, {a}, {a, c}, X } and observe that cl({a}) = X . If we choose the minimal ideal I = {;} on X , then the singleton subset {b} is not I − β-open, as there is no preopen set G satisfying G \ {b} ∈ I and {b} \ cl(G) ∈ I, simultaneously. Proposition 4. Let A a ...
... Example 2. Consider X = {a, b, c} and τ = {;, {a}, {a, c}, X } and observe that cl({a}) = X . If we choose the minimal ideal I = {;} on X , then the singleton subset {b} is not I − β-open, as there is no preopen set G satisfying G \ {b} ∈ I and {b} \ cl(G) ∈ I, simultaneously. Proposition 4. Let A a ...
Topological spaces
... examples of topological spaces X that have subsets A that are neither open nor closed as well as subsets B that are both open and closed. Certainly B = ∅ and B = X are examples of the latter. Definition 1.3. Given a set X and two topologies T1 and T2 on X, we say that T1 is finer than T2 or, equival ...
... examples of topological spaces X that have subsets A that are neither open nor closed as well as subsets B that are both open and closed. Certainly B = ∅ and B = X are examples of the latter. Definition 1.3. Given a set X and two topologies T1 and T2 on X, we say that T1 is finer than T2 or, equival ...
On topological groups via a-local functions - RiuNet
... Vaidyanathaswamy [18]. Jankovic and Hamlett [10] investigated further properties of ideal space. In this paper, we investigate a-local functions and its properties in ideals in topological space [1]. Also, the relationships among local functions such as local function [19, 10] and semi-local functio ...
... Vaidyanathaswamy [18]. Jankovic and Hamlett [10] investigated further properties of ideal space. In this paper, we investigate a-local functions and its properties in ideals in topological space [1]. Also, the relationships among local functions such as local function [19, 10] and semi-local functio ...
STRATIFIED SPACES TWIGS 1. Introduction These
... from the definition, and a stratification satisfying the axiom of the frontier is called a primary stratification. However, the above definition seems to require the least while still being useful, and so we will use it. 3. Examples There are many examples of such spaces, and in fact this is the mai ...
... from the definition, and a stratification satisfying the axiom of the frontier is called a primary stratification. However, the above definition seems to require the least while still being useful, and so we will use it. 3. Examples There are many examples of such spaces, and in fact this is the mai ...