The R-completion of closure spaces

2021 ◽  
pp. 107873
Author(s):  
Zhongxi Zhang ◽  
Fu-Gui Shi ◽  
Qingguo Li
Keyword(s):  
Closure Spaces

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.

Simple games on closure spaces

Top ◽  
2000 ◽  
Vol 8 (1) ◽  
pp. 43-55 ◽  
Author(s):  
J. M. Bilbao ◽  
E. Lebrón ◽  
N. Jiménez
Keyword(s):  
Simple Games ◽  
Closure Spaces

scholarly journals Soft Continuous Mappings in Soft Closure Spaces

2021 ◽  
pp. 2676-2684
Author(s):  
S. T. Ekram ◽  
R. N. Majeed
Keyword(s):  
Closure Operators ◽  
Continuous Mappings ◽  
Closure Spaces

Soft closure spaces are a new structure that was introduced very recently. These new spaces are based on the notion of soft closure operators. This work aims to provide applications of soft closure operators. We introduce the concept of soft continuous mappings and soft closed (resp. open) mappings, support them with examples, and investigate some of their properties.

scholarly journals On complete objects in the category of T0 closure spaces

2003 ◽  
Vol 4 (1) ◽  
pp. 25 ◽  
Author(s):  
D. Deses ◽  
Eraldo Giuli ◽  
E. Lowen-Colebunders
Keyword(s):  
General Theory ◽  
Complete Lattices ◽  
Closure Spaces

<p>In this paper we present an example in the setting of closure spaces that fits in the general theory on “complete objects” as developed by G. C. L. Brümmer and E. Giuli. For V the class of epimorphic embeddings in the construct Cl<sub>0</sub> of T<sub>0</sub> closure spaces we prove that the class of V-injective objects is the unique firmly V-reflective subconstruct of Cl0. We present an internal characterization of the Vinjective objects as “complete” ones and it turns out that this notion of completeness, when applied to the topological setting is much stronger than sobriety. An external characterization of completeness is obtained making use of the well known natural correspondence of closures with complete lattices. We prove that the construct of complete T<sub>0</sub> closure spaces is dually equivalent to the category of complete lattices with maps preserving the top and arbitrary joins.</p>

M-Fuzzifying Approximation Spaces, M-Fuzzifying Pretopological Spaces and M-Fuzzifying Closure Spaces

2020 ◽  
Vol 16 (03) ◽  
pp. 609-626
Author(s):  
Anand P. Singh ◽  
I. Perfilieva
Keyword(s):  
Significant Role ◽  
Category Theory ◽  
Galois Connection ◽  
Fuzzy Relations ◽  
Approximation Spaces ◽  
Closure Spaces

In category theory, Galois connection plays a significant role in developing the connections among different structures. The objective of this work is to investigate the essential connections among several categories with a weaker structure than that of [Formula: see text]-fuzzifying topology, viz. category of [Formula: see text]-fuzzifying approximation spaces based on reflexive [Formula: see text]-fuzzy relations, category of [Formula: see text]-fuzzifying pretopological spaces and the category of [Formula: see text]-fuzzifying interior (closure) spaces. The interrelations among these structures are shown via the functorial diagram.

A unified method for completions of posets and closure spaces

2019 ◽  
Vol 23 (21) ◽  
pp. 10699-10708 ◽  
Author(s):  
Zhongxi Zhang ◽  
Qingguo Li ◽  
Nan Zhang
Keyword(s):  
Closure Spaces ◽  
Unified Method

scholarly journals Closure spaces and characterizations of filters in terms of their stone images

2007 ◽  
Vol 57 (3) ◽  
pp. 1025-1034 ◽  
Author(s):  
Anh Tran Mynard ◽  
Frédéric Mynard
Keyword(s):  
Closure Spaces

scholarly journals Near Approximations in -Closure Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-23
Author(s):  
M. E. Abd El-Monsef ◽  
M. Shokry ◽  
Y. Y. Yousif
Keyword(s):  
Mathematical Models ◽  
Real Life ◽  
Approximation Spaces ◽  
Closure Approximation ◽  
Closure Spaces

Most real-life situations need some sort of approximation to fit mathematical models. The beauty of using topology in approximation is achieved via obtaining approximation for qualitative subgraphs without coding or using assumption. The aim of this paper is to apply near concepts in the -closure approximation spaces. The basic notions of near approximations are introduced and sufficiently illustrated. Near approximations are considered as mathematical tools to modify the approximations of graphs. Moreover, proved results, examples, and counterexamples are provided.

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