Fuzzy Semi-Connectedness and Fuzzy Pre-Connectedness in Fuzzy Closure Space

2015 ◽  
Vol 5 (2) ◽  
pp. 83
Author(s):  
U. D. Tapi ◽  
A. Deole Bhagyashri
Keyword(s):  
Closure Space

scholarly journals Some Variants of Normal Čech Closure Spaces via Canonically Closed Sets

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1225
Author(s):  
Ria Gupta ◽  
Ananga Kumar Das
Keyword(s):  
Closure Space ◽  
Closed Sets ◽  
Closure Spaces

New generalizations of normality in Čech closure space such as π-normal, weakly π-normal and κ-normal are introduced and studied using canonically closed sets. It is observed that the class of κ-normal spaces contains both the classes of weakly π-normal and almost normal Čech closure spaces.

Representations of presheaves of closure space

1972 ◽  
Vol 22 (1) ◽  
pp. 7-48
Author(s):  
Jaroslav Pechanec-Drahoš
Keyword(s):  
Closure Space

On normality of a closure space generated from a tree by relation

2021 ◽  
pp. 2250110
Author(s):  
A. K. Das ◽  
Ria Gupta
Keyword(s):  
Comparative Study ◽  
Binary Relation ◽  
Applied Mathematics ◽  
Closure Space ◽  
Topological Properties ◽  
Closure Spaces

Binary relation plays a prominent role in the study of mathematics in particular applied mathematics. Recently, some authors generated closure spaces through relation and made a comparative study of topological properties in the space by varying the property on the relation. In this paper, we have studied closure spaces generated from a tree through binary relation and observed that under certain situation the space generated from a tree is normal.

Topological modification of a fuzzy closure space

1988 ◽  
Vol 27 (2) ◽  
pp. 211-215 ◽  
Author(s):  
M.H. Ghanim ◽  
Fatma S. Al-Sirehy
Keyword(s):  
Closure Space

scholarly journals Strongly Connectedness in Closure Space

2014 ◽  
Vol 9 ◽  
pp. 69-71
Author(s):  
U.D. Tapi ◽  
Bhagyashri A. Deole
Keyword(s):  
Topological Space ◽  
Disjoint Union ◽  
Closure Operator ◽  
Closure Space ◽  
Closed Set ◽  
Power Set ◽  
Strongly Connected

A Čech closure space (X, u) is a set X with Čech closure operator u: P(X) → P(X) where P(X) is a power set of X, which satisfies u𝝓=𝝓, A ⊆uA for every A⊆X, u (A⋃B) = uA⋃uB, for all A, B ⊆ X. Many properties which hold in topological space hold in closure space as well. A topological space X is strongly connected if and only if it is not a disjoint union of countably many but more than one closed set. If X is strongly connected, and Ei‟s are nonempty disjoint closed subsets of X, then X≠ E1∪E2∪. We further extend the concept of strongly connectedness in closure space. The aim of this paper is to introduce and study the concept of strongly connectedness in closure space.

scholarly journals Extensions of closure spaces

2003 ◽  
Vol 4 (2) ◽  
pp. 223
Author(s):  
D. Deses ◽  
A. De Groot-Van der Voorde ◽  
E. Lowen-Colebunders
Keyword(s):  
Closure Operator ◽  
Finite Additivity ◽  
Closure Space ◽  
Closure Spaces ◽  
The One ◽  
Separation Conditions

<p>A closure space X is a set endowed with a closure operator P(X) → P(X), satisfying the usual topological axioms, except finite additivity. A T<sub>1</sub> closure extension Y of a closure space X induces a structure ϒ on X satisfying the smallness axioms introduced by H. Herrlich [?], except the one on finite unions of collections. We'll use the word seminearness for a smallness structure of this type, i.e. satisfying the conditions (S1),(S2),(S3) and (S5) from [?]. In this paper we show that every T<sub>1</sub> seminearness structure ϒ on X can in fact be induced by a T<sub>1</sub> closure extension. This result is quite different from its topological counterpart which was treated by S.A. Naimpally and J.H.M. Whitfield in [?]. Also in the topological setting the existence of (strict) extensions satisfying higher separation conditions such as T<sub>2</sub> and T<sub>3</sub> has been completely characterized by means of concreteness, separatedness and regularity [?]. In the closure setting these conditions will appear to be too weak to ensure the existence of suitable (strict) extensions. In this paper we introduce stronger alternatives in order to present internal characterizations of the existence of (strict) T<sub>2</sub> or strict regular closure extensions.</p>

scholarly journals On the lattice of proximities of Čech compatible with a given closure space

1973 ◽  
Vol 49 (2) ◽  
pp. 519-535 ◽  
Author(s):  
W. J. Thron ◽  
Richard Warren
Keyword(s):  
Closure Space

A study of generalized closed set in the closure space

2022 ◽  
Author(s):  
Neeran Tahir Abd Alameer ◽  
Shahad Safy Hussein
Keyword(s):  
Closure Space ◽  
Closed Set
Sign in / Sign up

Export Citation Format

Share Document