NEW TYPES OF SETS IN CECH 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.

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STATE PROPERTY SYSTEMS AND CLOSURE SPACES: EXTRACTING THE CLASSICAL EN NONCLASSICAL PARTS

Probing the Structure of Quantum Mechanics ◽

10.1142/9789812778024_0006 ◽

2002 ◽

Cited By ~ 2

Author(s):

DIEDERIK AERTS ◽

DIDIER DESES

Keyword(s):

Closure Spaces

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Simple games on closure spaces

Top ◽

10.1007/bf02564827 ◽

2000 ◽

Vol 8 (1) ◽

pp. 43-55 ◽

Cited By ~ 1

Author(s):

J. M. Bilbao ◽

E. Lebrón ◽

N. Jiménez

Keyword(s):

Simple Games ◽

Closure Spaces

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Soft Continuous Mappings in Soft Closure Spaces

Iraqi Journal of Science ◽

10.24996/ijs.2021.62.8.20 ◽

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.

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On complete objects in the category of T0 closure spaces

Applied General Topology ◽

10.4995/agt.2003.2007 ◽

2003 ◽

Vol 4 (1) ◽

pp. 25 ◽

Cited By ~ 6

Author(s):

D. Deses ◽

Eraldo Giuli ◽

E. Lowen-Colebunders

Keyword(s):

General Theory ◽

Complete Lattices ◽

Closure Spaces

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 Cl0 of T0 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 T0 closure spaces is dually equivalent to the category of complete lattices with maps preserving the top and arbitrary joins.

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The R-completion of closure spaces

Topology and its Applications ◽

10.1016/j.topol.2021.107873 ◽

2021 ◽

pp. 107873

Author(s):

Zhongxi Zhang ◽

Fu-Gui Shi ◽

Qingguo Li

Keyword(s):

Closure Spaces

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

New Mathematics and Natural Computation ◽

10.1142/s1793005720500374 ◽

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.

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