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.

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.

scholarly journals Some Variants of Strong Normality in Closure Spaces Generated via Relations

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Ria Gupta ◽  
Ananga Kumar Das
Keyword(s):  
Binary Relation ◽  
Normal Closure ◽  
Separation Axioms ◽  
Closure Spaces ◽  
Strong Normality

In this paper, some variants of strongly normal closure spaces obtained by using binary relation are introduced, and examples in support of existence of the variants are provided by using graphs. The relationships that exist between variants of strongly normal closure spaces and covering axioms in absence/presence of lower separation axioms are investigated. Further, closure subspaces and preservation of the properties studied under mapping are also discussed.

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>

Representation of bifinite domains by BF-closure spaces

2021 ◽  
Vol 71 (3) ◽  
pp. 565-572
Author(s):  
Lingjuan Yao ◽  
Qingguo Li
Keyword(s):  
Continuous Functions ◽  
Closure Space ◽  
Closed Sets ◽  
Set Inclusion ◽  
Closure Spaces ◽  
Scott Continuous

Abstract In this paper, we propose the notion of BF-closure spaces as concrete representation of bifinite domains. We prove that every bifinite domain can be obtained as the set of F-closed sets of some BF-closure space under set inclusion. Furthermore, we obtain that the category of bifinite domains and Scott-continuous functions is equivalent to that of BF-closure spaces and F-morphisms.

scholarly journals Some properties of hyperspaces of Cech closure spaces with Vietoris-like topologies

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 53-61 ◽  
Author(s):  
Dimitrije Andrijevic ◽  
Milena Jelic ◽  
Mila Mrsevic
Keyword(s):  
Topological Properties ◽  
Selection Principles ◽  
Closure Spaces

We study some topological properties of hyperspaces of Cech closure spaces endowed with Vietoris-like topologies. Some of these notions were introduced and considered in [9, 10] and [11], focussing on selection principles.

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