About the ways of defining connected sets in the topological spaces

In this paper we introduce some types of generalized fuzzy soft separated sets and study some of their properties. Next, the notion of connectedness in fuzzy soft topological spaces due to Karata et al, Mahanta et al, and Kandil et al., extended to generalized fuzzy soft topological spaces. The relationship between these types of connectedness in generalized fuzzy soft topological spaces is investigated with the help of number of counter examples.

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Weakly chain separated sets in a topological space

Mathematica Montisnigri ◽

10.20948/mathmontis-2021-52-1 ◽

2021 ◽

Vol 52 ◽

pp. 5-16

Author(s):

Nikita Shekutkovski ◽

Zoran Misajleski ◽

Aneta Velkoska ◽

Emin Durmishi

Keyword(s):

Topological Space ◽

Topological Spaces ◽

Connected Sets ◽

Connected Set ◽

Separated Sets ◽

Better Than

In this paper we introduce the notion of pair of weakly chain separated sets in a topological space. If two sets are chain separated in the topological space, then they are weakly chain separated in the same space. We give an example of weakly chain separated sets in a topological space that are not chain separated in the space. Then we study the properties of these sets. Also we mention the criteria for two kind of topological spaces by using the notion of chain. The topological space is totally separated if and only if any two different singletons (unit subsets) are weakly chain separated in the space, and it is the discrete if and only if any pair of different nonempty subsets are chain separated. Moreover we give a criterion for chain connected set in a topological space by using the notion of weakly chain separateness. This criterion seems to be better than the criterion of chain connectedness by using the notion of pair of chain separated sets. Then we prove the properties of chain connected, and as a consequence of connected sets in a topological space by using the notion of weakly chain separateness.

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\mu-\mu^{*} - Connectedness via Hereditary Classes

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.v33i1.21383 ◽

2013 ◽

Vol 33 (1) ◽

pp. 41

Author(s):

Shyamapada Modak

Keyword(s):

Topological Spaces ◽

Hereditary Class ◽

Connected Sets ◽

Connected Set ◽

Separated Sets

This paper is an attempt to study and introduce the notion of - - connected set in generalized topological spaces with a hereditary class. We have also investigate the relationships between -separated sets, s - connected sets, c -I - connected sets, c -c -connected sets, c-I - connected sets, -I - connected sets. Further we give some representations of the above connected sets via (-0) - continuity and (-0) - openness.

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Fuzzy Soft Connected Sets in Fuzzy Soft Topological Spaces

JOURNAL OF ADVANCES IN MATHEMATICS ◽

10.24297/jam.v12i8.136 ◽

2016 ◽

Vol 12 (8) ◽

pp. 6473-6888 ◽

Cited By ~ 4

Author(s):

A Kandil ◽

O. A. E Tantawy

Keyword(s):

Topological Spaces ◽

Connected Sets ◽

Fuzzy Topological Spaces ◽

Separated Sets ◽

The Relationship

In this paper we introduce some types of fuzzy soft separated sets and study some of thier preperties. Next, the notion of connectedness in fuzzy topological spaces due to Ming and Ming, Zheng etc., extended to fuzzy soft topological spaces. The relationship between these types of connectedness in fuzzy soft topological spaces is investigated with the help of number of counter examples.

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On soft P_c-connected spaces

Iraqi Journal of Science ◽

10.24996/ijs.2020.61.11.28 ◽

2020 ◽

pp. 3061-3070

Author(s):

Qumri H. Hamko ◽

Nehmat K. Ahmed ◽

Alias B. Khalaf

Keyword(s):

Topological Spaces ◽

Connected Sets ◽

Connected Spaces

In this paper, we define the concept of soft -connected sets and soft -connected spaces by using the notion of soft -open sets in soft topological spaces. Several properties of these concepts are investigated.

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Connectedness and Stratification of Single-Valued Neutrosophic Topological Spaces

Symmetry ◽

10.3390/sym12091464 ◽

2020 ◽

Vol 12 (9) ◽

pp. 1464

Author(s):

Yaser Saber ◽

Fahad Alsharari ◽

Florentin Smarandache ◽

Mohammed Abdel-Sattar

Keyword(s):

Topological Spaces ◽

Basic Properties ◽

Intuitionistic Fuzzy ◽

Connected Sets ◽

Fuzzy Topological Spaces

This paper aims to introduce the notion of r-single-valued neutrosophic connected sets in single-valued neutrosophic topological spaces, which is considered as a generalization of r-connected sets in Šostak’s sense and r-connected sets in intuitionistic fuzzy topological spaces. In addition, it introduces the concept of r-single-valued neutrosophic separated and obtains some of its basic properties. It also tries to show that every r-single-valued neutrosophic component in single-valued neutrosophic topological spaces is an r-single-valued neutrosophic component in the stratification of it. Finally, for the purpose of symmetry, it defines the so-called single-valued neutrosophic relations.

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An extension problem of a connectedness preserving map between Khalimsky spaces

Filomat ◽

10.2298/fil1601015h ◽

2016 ◽

Vol 30 (1) ◽

pp. 15-28 ◽

Cited By ~ 1

Author(s):

Sang-Eon Han

Keyword(s):

Computer Science ◽

Mathematical Morphology ◽

Digital Images ◽

Digital Topology ◽

Extension Problem ◽

Topological Spaces ◽

Digital Geometry ◽

Applied Topology ◽

Continuous Map ◽

Connected Sets

The goal of the present paper is to study an extension problem of a connected preserving (for short, CP-) map between Khalimsky (K-for brevity, if there is no ambiguity) spaces. As a generalization of a K-continuous map, for K-topological spaces the recent paper [13] develops a function sending connected sets to connected ones (for brevity, an A-map: see Definition 3.1 in the present paper). Since this map plays an important role in applied topology including digital topology, digital geometry and mathematical morphology, the present paper studies an extension problem of a CP-map in terms of both an A-retract and an A-isomorphism (see Example 5.2). Since K-topological spaces have been often used for studying digital images, this extension problem can contribute to a certain areas of computer science and mathematical morphology.

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