A new approach of semiregular compactness in L-topological spaces

2012 ◽  
Author(s):  
Bo Chen
Keyword(s):  
Topological Spaces ◽  
New Approach

A New Approach to Generalized Fuzzy Topological Spaces

2015 ◽  
Author(s):  
Baby Bhattacharya ◽  
Jayasree Chakraborty ◽  
Arnab Paul
Keyword(s):  
Topological Spaces ◽  
New Approach ◽  
Fuzzy Topological Spaces

scholarly journals A New Approach to Rough Set Based on Remote Neighborhood Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Shoubin Sun ◽  
Lingqiang Li ◽  
Kai Hu
Keyword(s):  
Rough Set ◽  
Topological Spaces ◽  
New Approach ◽  
Upper Approximation ◽  
Basic Properties ◽  
Approximation Operators ◽  
Dual Notion

The notion of neighborhood systems is abstracted from the geometric notion of “near”, and it is primitive in the theory of topological spaces. Now, neighborhood systems have been applied in the study of rough set by many researches. The notion of remote neighborhood systems is initial in the theory of topological molecular lattice, and it is abstracted from the geometric notion of “remote”. Therefore, the notion of remote neighborhood systems can be considered as the dual notion of neighborhood systems. In this paper, we develop a theory of rough set based on remote neighborhood systems. Precisely, we construct a pair of lower and upper approximation operators and discuss their basic properties. Furthermore, we use a set of axioms to describe the lower and upper approximation operators constructed from remote neighborhood systems.

scholarly journals Persistent Homology applied to location problems

2018 ◽  
Vol 200 ◽  
pp. 00003
Author(s):  
Driss Bennis ◽  
Fouad Gharib ◽  
Ghita Lebbar
Keyword(s):  
Material Science ◽  
Persistent Homology ◽  
Location Problems ◽  
Topological Data Analysis ◽  
Topological Spaces ◽  
Design Problems ◽  
New Approach ◽  
Homology Groups ◽  
Research Areas ◽  
Processing Material

Different approaches to solve location problems in transport and logistics have been developed in the literature. This article introduces a new approach using the concept of persistent homology which has been proved to be an efficient method in topological data analysis; and has been served as an alternative new tool in many and various research areas such as image processing, material science and biological systems. Precisely, inspired by the notions of the first homology groups and the persistent homology which mainly describe the behaviour of connectivity relation between elements during a filtration of specific topological spaces; we develop a new method and approach for the treatment of facility location–network design problems.

Proximate topology and shape theory

1995 ◽  
Vol 125 (3) ◽  
pp. 595-615 ◽  
Author(s):  
Zvonko Čerin
Keyword(s):  
Metric Spaces ◽  
Topological Spaces ◽  
Shape Theory ◽  
Homotopy Classes ◽  
New Approach ◽  
Compact Metric Spaces ◽  
Shape Category

Most of the development of shape theory was in the so-called outer shape theory, where the shape of spaces is described with the help of some outside objects.This paper belongs to the so-called inner shape theory, in which the shape of spaces is described intrinsically without the use of any outside gadgets. We give a description of shape theory that does not need absolute neighbourhood retracts. We prove that the category ℋN whose objects are topological spaces and whose morphisms are proximate homotopy classes of proximate nets is naturally equivalent to the shape category h. The description of the category ℋN for compact metric spaces was given earlier by José M. R. Sanjurjo. We also give three applications of this new approach to shape theory.

scholarly journals A new approach to nearly compact spaces

2018 ◽  
Vol 22 (1) ◽  
pp. 137-147
Author(s):  
Kallol Bhandhu Bagchi ◽  
Ajoy Mukharjee ◽  
Madhusudhan Paul
Keyword(s):  
Topological Spaces ◽  
New Approach ◽  
Compact Spaces

Using the covers formed by pre-open sets, we introduce and study the notion of po-compactness in topological spaces. The notion of po-compactness is weaker than that of compactness but stronger than semi-compactness. It is observed that po-compact spaces are the same as nearly compact spaces. However, we find new characterizations to near compactness, when we study it in the sense of po-compactness.

A new approach to vague soft toplogical structures concerning soft points

2021 ◽  
pp. 1-17
Author(s):  
Arif Mehmood ◽  
Samer Al Ghour ◽  
Saleem Abdullah ◽  
Choonkil Park ◽  
Jung Rye Lee
Keyword(s):  
Topological Spaces ◽  
New Approach ◽  
Compact Spaces ◽  
Open Set ◽  
Separation Axioms ◽  
Topological Characteristics ◽  
Relationship Of ◽  
The Relationship

This paper concerns the study of the notion of vague soft β-open set and vague soft separation axioms in vague soft topological spaces. By using such notions and that of the vague soft pints, we study the separation axioms βi (with i = 0, 1, 2, 3, 4) in vague soft topological spaces. We give some peculiar examples about them and we prove some relationships between them. The relationship of βi (with i = , 1, 2, 3, 4) spaces with the closer of vague soft β-open set by means of soft points, vague soft countable spaces and their relationship with βi (with i = , 1, 2) spaces by means of soft points are addressed. In continuation, vague soft topological, vague soft inverse topological spaces properties, Bolzano Weirstrass Property(BVP) and its topological characteristics, compact spaces and sequentially compact spaces and their relationship with separation axioms by means soft points are addressed in vague soft topological spaces.

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