scholarly journals On soft P_c-connected spaces

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.

Local Connectedness of the stone-Čech Compactification

1988 ◽  
Vol 31 (2) ◽  
pp. 236-240 ◽  
Author(s):  
D. Baboolal
Keyword(s):  
Uniform Space ◽  
Finite Union ◽  
Local Connectedness ◽  
Connected Sets ◽  
Connected Spaces

AbstractA uniform space X is said to be uniformly locally connected if given any entourage U there exists an entourage V ⊂ U such that V[x] is connected for each x ∈ X. It is said to have property S if given any entourage U, X can be written as a finite union of connected sets each of which is U-small.Based on these two uniform connection properties, another proof is given of the following well known result in the theory of locally connected spaces: The Stone-Čech compactification βX is locally connected if and only if X is locally connected and pseudocompact.

Spaces on which every Continuous Map into a given Space is Constant

1986 ◽  
Vol 38 (6) ◽  
pp. 1281-1298 ◽  
Author(s):  
S. Iliadis ◽  
V. Tzannes
Keyword(s):  
Topological Spaces ◽  
Real Numbers ◽  
Continuous Map ◽  
Countable Space ◽  
Continuous Maps ◽  
Usual Topology ◽  
The Given ◽  
Connected Spaces

This paper is concerned with topological spaces whose continuous maps into a given space R are constant, as well as with spaces having this property locally. We call these spaces R-monolithic and locally R-monolithic, respectively.Spaces with such properties have been considered in [1], [5]-[7], [10], [11], [22], [28], [31], where with the exception of [10], the given space R is the set of real-numbers with the usual topology. Obviously, for a countable space, connectedness is equivalent to the property that every continuous real-valued map is constant. Countable connected (locally connected) spaces have been constructed in papers [2]-[4], [8], [9], [11]-[21], [23]-[26], [30].

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

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 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 Pythagorean Fuzzy Rough Connected Spaces

2021 ◽  
Vol 2070 (1) ◽  
pp. 012069
Author(s):  
P Revathi ◽  
R Radhamani
Keyword(s):  
Rough Set ◽  
Topological Spaces ◽  
Connected Space ◽  
Fuzzy Rough Set ◽  
Connected Spaces

Abstract In this paper Pythagorean fuzzy rough set and Pythagorean fuzzy rough topological spaces are defined for the connected space. Then, the properties of connectedness are discussed with examples.

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.

Preference orders and continuous representations

2011 ◽  
Vol 61 (1) ◽  
Author(s):  
Alessandro Caterino ◽  
Rita Ceppitelli ◽  
Ghanshyam Mehta
Keyword(s):  
Representation Theorem ◽  
Topological Spaces ◽  
Continuous Representation ◽  
Representation Theorems ◽  
Preference Orders ◽  
Separable Spaces ◽  
Path Connected ◽  
Continuous Representations ◽  
Connected Spaces

AbstractIn this paper we prove some general theorems on the existence of continuous order-preserving functions on topological spaces with a continuous preorder. We use the concepts of network and netweight to prove new continuous representation theorems and we establish our main results for topological spaces that are countable unions of subspaces. Some results in the literature on path-connected, locally connected and separably connected spaces are shown to be consequences of the general theorems proved in the paper. Finally, we prove a continuous representation theorem for hereditarily separable spaces.

scholarly journals On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces

Mathematics ◽  
2018 ◽  
Vol 7 (1) ◽  
pp. 1 ◽  
Author(s):  
Wadei Al-Omeri ◽  
Saeid Jafari
Keyword(s):  
The Other ◽  
Topological Spaces ◽  
Compact Spaces ◽  
Extremally Disconnected ◽  
Closed Sets ◽  
Connected Spaces

In this paper, the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets. In addition, we discuss some applications of generalized neutrosophic pre-closed sets, namely neutrosophic p T 1 2 space and neutrosophic g p T 1 2 space. The concepts of generalized neutrosophic connected spaces, generalized neutrosophic compact spaces and generalized neutrosophic extremally disconnected spaces are established. Some interesting properties are investigated in addition to giving some examples.

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