scholarly journals Generalized Fuzzy Soft Connected Sets in Generalized Fuzzy Soft Topological Spaces

2018 ◽  
Vol 14 (2) ◽  
pp. 7787-7805
Author(s):  
Mohammed Saleh Malfi ◽  
Fathi Hishem Khedr ◽  
Mohamad Azab Abd Allah
Keyword(s):  
Topological Spaces ◽  
Connected Sets ◽  
Separated Sets ◽  
The Relationship

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.

scholarly journals Fuzzy Soft Connected Sets in Fuzzy Soft Topological Spaces

2016 ◽  
Vol 12 (8) ◽  
pp. 6473-6888 ◽  
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.

scholarly journals Weakly chain separated sets in a topological space

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.

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

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.

scholarly journals \mu - k - Connectedness in GTS

2014 ◽  
Vol 33 (2) ◽  
pp. 161-165
Author(s):  
Shyamapada Modak ◽  
Takashi Noiri
Keyword(s):  
Connected Sets ◽  
Separated Sets

Csaszar [4] introduced \mu - semi - open sets, \mu - preopen sets, \mu - \alpha - open sets and \mu - \beta - open sets in a GTS (X, \tau). By using the \mu - \sigma - closure, \mu - \pi - closure, \mu - \alpha - closure and \mu - \beta - closure in (X, \tau), we introduce and investigate the notions \mu - k - separated sets and \mu - k - connected sets in (X, \tau).

scholarly journals On t-Neighbourhoods in Trigonometric Topological Spaces

2021 ◽  
Vol 12 (1S) ◽  
pp. 655-658
Author(s):  
S. Malathi, Et. al.
Keyword(s):  
Necessary Condition ◽  
Topological Spaces ◽  
Basic Properties ◽  
New Type ◽  
The Relationship

In this paper we introduce a new type of neighbourhoods, namely, t-neighbourhoods in trigonometric topological spaces and study their basic properties. Also, we discuss the relationship between neighbourhoods and t-neighbourhoods. Further, we give the necessary condition for t-neighbourhoods in trigonometric topological spaces.  .

scholarly journals Convergence Classes of L -Filters in L , M -Fuzzy Topological Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Ting Yang ◽  
Sheng-Gang Li ◽  
William Zhu ◽  
Xiao-Fei Yang ◽  
Ahmed Mostafa Khalil
Keyword(s):  
Topological Spaces ◽  
Convergence Spaces ◽  
Topological Convergence ◽  
Convergence Structure ◽  
Fuzzy Topological Spaces ◽  
The Relationship

An L , M -fuzzy topological convergence structure on a set X is a mapping which defines a degree in M for any L -filter (of crisp degree) on X to be convergent to a molecule in L X . By means of L , M -fuzzy topological neighborhood operators, we show that the category of L , M -fuzzy topological convergence spaces is isomorphic to the category of L , M -fuzzy topological spaces. Moreover, two characterizations of L -topological spaces are presented and the relationship with other convergence spaces is concretely constructed.

Localization, Algebraic Loops and H-Spaces I

1979 ◽  
Vol 31 (2) ◽  
pp. 427-435 ◽  
Author(s):  
Albert O. Shar
Keyword(s):  
Nilpotent Group ◽  
Algebraic Structure ◽  
Nilpotent Groups ◽  
Topological Spaces ◽  
Finitely Generated ◽  
Cw Complex ◽  
Topological Localization ◽  
The Relationship

If (Y, µ) is an H-Space (here all our spaces are assumed to be finitely generated) with homotopy associative multiplication µ. and X is a finite CW complex then [X, Y] has the structure of a nilpotent group. Using this and the relationship between the localizations of nilpotent groups and topological spaces one can demonstrate various properties of [X,Y] (see [1], [2], [6] for example). If µ is not homotopy associative then [X, Y] has the structure of a nilpotent loop [7], [9]. However this algebraic structure is not rich enough to reflect certain significant properties of [X, Y]. Indeed, we will show that there is no theory of localization for nilpotent loops which will correspond to topological localization or will restrict to the localization of nilpotent groups.

scholarly journals Neighbourhood lattices – a poset approach to topological spaces

1989 ◽  
Vol 39 (1) ◽  
pp. 31-48 ◽  
Author(s):  
Frank P. Prokop
Keyword(s):  
Topological Space ◽  
Lattice Structure ◽  
Algebraic Closure ◽  
Topological Spaces ◽  
Closure Operators ◽  
Continuity Properties ◽  
Image Function ◽  
Topological Closure ◽  
Arbitrary Lattice ◽  
The Relationship

In this paper neighbourhood lattices are developed as a generalisation of topological spaces in order to examine to what extent the concepts of “openness”, “closedness”, and “continuity” defined in topological spaces depend on the lattice structure of P(X), the power set of X.A general pre-neighbourhood system, which satisfies the poset analogues of the neighbourhood system of points in a topological space, is defined on an ∧-semi-lattice, and is used to define open elements. Neighbourhood systems, which satisfy the poset analogues of the neighbourhood system of sets in a topological space, are introduced and it is shown that it is the conditionally complete atomistic structure of P(X) which determines the extension of pre-neighbourhoods of points to the neighbourhoods of sets.The duals of pre-neighbourhood systems are used to generate closed elements in an arbitrary lattice, independently of closure operators or complementation. These dual systems then form the backdrop for a brief discussion of the relationship between preneighbourhood systems, topological closure operators, algebraic closure operators, and Čech closure operators.Continuity is defined for functions between neighbourhood lattices, and it is proved that a function f: X → Y between topological spaces is continuous if and only if corresponding direct image function between the neighbourhood lattices P(X) and P(Y) is continuous in the neighbourhood sense. Further, it is shown that the algebraic character of continuity, that is, the non-convergence aspects, depends only on the properites of pre-neighbourhood systems. This observation leads to a discussion of the continuity properties of residuated mappings. Finally, the topological properties of normality and regularity are characterised in terms of the continuity properties of the closure operator on a topological space.

scholarly journals Fuzzy soft connected sets in fuzzy soft topological spaces II

2017 ◽  
Vol 25 (2) ◽  
pp. 171-177 ◽  
Author(s):  
A. Kandil ◽  
O.A. El-Tantawy ◽  
S.A. El-Sheikh ◽  
Sawsan S.S. El-Sayed
Keyword(s):  
Topological Spaces ◽  
Connected Sets
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