Some Special Conditions in Topological Summed

Atay, Arife; Tutalar, H İlhan

doi:10.17148/iarjset.2015.21027

International Advanced Research Journal in Science, Engineering

2015

DOI: 10.17148/iarjset.2015.21027

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Some Special Conditions in Topological Summed

Arife Atay¹,

H İlhan Tutalar²

Abstract: This study includes free union of a disjoint non-empty collection of topological spaces and research on the disjoint union topology (topological summed). Definitions, theorems and some results for topological summed have been obtained by using the known definitions and theorems for the topological spaces.

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2023

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Disjoint union of fuzzy soft topological spaces

Atay

2023

MATH

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<abstract><p>In this work, sums of fuzzy soft topological spaces are defined with free union of a pairwise disjoint non-empty family of fuzzy soft topological spaces. Firstly, we give general information of fuzzy soft topological spaces. Then, we define free union of fuzzy soft topological spaces and disjoint union topology of fuzzy soft topological spaces. We call the free union of a pairwise disjoint non-empty family of fuzzy soft topological spaces the sum of fuzzy soft topological spaces. We show what are the interchangeable properties between fuzzy soft topological spaces and the sum of fuzzy soft topological spaces. For example, there are fuzzy soft interior, fuzzy soft closure, fuzzy soft limit points. Also, we provide some properties showing the relationships between fuzzy soft topological spaces and their sums. Some of these are fuzzy soft base, fuzzy soft sequences, fuzzy soft connected-disconnected, fuzzy soft compact spaces. Also, part of the research for this article is work on fuzzy soft convergence on fuzzy soft topological sum. With this paper, some results, theorems and definitions for fuzzy soft topological sum have been acquired with the help of results, theorems and definitions given in previous studies about fuzzy soft topological spaces.</p></abstract>

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Disjoint union of fuzzy soft topological spaces

Atay

2023

MATH

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Some Special Conditions in Topological Summed

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Disjoint union of fuzzy soft topological spaces

Disjoint union of fuzzy soft topological spaces

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