Introduction to Neutrosophic Soft Bitopological Spaces

2021 ◽  
Author(s):  
Hasan Dadas ◽  
◽  
Sibel Demiralp ◽  
Keyword(s):  
Bitopological Space ◽  
Closed Set ◽  
Soft Topology ◽  
The Subject ◽  
Bitopological Spaces

In this study, the concept of neutrosophic soft bitopological space is defined and it is one of the few studies that have dealt with this concept. In addition, pairwise neutrosophic soft open (closed) set on neutrosophic soft bitopological spaces are studied. Supra neutrosophic soft topology is defined by pairwise neutrosophic soft open sets. Important theorems related to the subject supported with many examples for a better understanding of the subject are given.

scholarly journals On Lembda Gamma- Set in Fuzzy Bitopological Spaces

2017 ◽  
Vol 35 (3) ◽  
pp. 285 ◽  
Author(s):  
Arnab Paul ◽  
Arnab Paul ◽  
Baby Bhattacharya ◽  
Jayasree Chakraborty
Keyword(s):  
Fuzzy Set ◽  
Bitopological Space ◽  
Closed Set ◽  
Generalized Continuity ◽  
Bitopological Spaces

The aim of this paper is to introduce the concept of lambda operator of a fuzzy set in a fuzzy bitopological space.  Then we study (i, j)-fuzzy Lembda Gamma- set and its properties. Moreover we define (i, j)-fuzzy Lembda-closed set, (i, j)-fuzzy Lembda Gamma-closed set and (i, j)-fuzzy generalized closed set in fuzzy bitopological space. The concepts (i, j)-fuzzy Lembda-closed set and (i, j)-fuzzy generalized closed set are independent to each other but jointly they gives the taui-fuzzy closed set. To this end as the application of (i, j)-fuzzy Lembda Gamma-closed set we shall study (i, j)-fuzzy Lembda Gamma continuity and (i, j)-fuzzy Lembda Gamma-generalized continuity and their properties.

R1, Pairwise Compact, and Pairwise Complete Spaces

1972 ◽  
Vol 15 (1) ◽  
pp. 109-113 ◽  
Author(s):  
G. D. Richardson
Keyword(s):  
Topological Spaces ◽  
Bitopological Space ◽  
Closed Set ◽  
Usual Definition ◽  
Local Compactness ◽  
Definition Of ◽  
Bitopological Spaces

The R1 axiom was first introduced by Davis in [1]. It is strictly weaker than the T2 axiom. Murdeshwar and Naimpally, in [4], have weakened the T2 hypothesis to R1 in some well-known theorems. We show that in many topological spaces the R1 axiom and regularity are equivalent. Also, the definition of local compactness given in [4] can be weakened to the usual definition and still get the same results.The notion of a bitopological space was first introduced by Kelley in [3]. Fletcher, Hoyle, and Patty discuss pairwise compactness for bitopological spaces in [2]. One of our main results is that a bitopological space (X, P, Q) is pairwise compact if and only if each ultrafilter v on X, containing a proper P closed set and a proper Q closed set, has a common P and Q limit.

scholarly journals Neutrosophic Soft Bitopological Spaces

2021 ◽  
Author(s):  
Ahmed B. AL-Nafee ◽  
◽  
Said Broumi ◽  
Florentin Smarandache ◽  
◽  
...  
Keyword(s):  
Soft Set ◽  
Topological Spaces ◽  
Bitopological Space ◽  
Closed Set ◽  
Open Set ◽  
Bitopological Spaces

In this paper, we built bitopological space on the concept of neutrosophic soft set, we defined the basic topological concepts of this spaces which are N3-(bi)*-open set, N3-(bi)*-closed set, (bi)*-neutrosophic soft interior, (bi)* neutrosophic soft closure, (bi)*-neutrosophic soft boundary, (bi)*-neutrosophic soft exterior and we introduced their properties. In addition, we investigated the relations of these basic topological concepts with their counterparts in neutrosophic soft topological spaces and we introduced many examples.

scholarly journals DISCUSSION ON QUOTIENT BI-SPACE AND ON PAIRWISE REGULAR AND NORMAL SPACES IN BITOPOLOGICAL SPACES

2019 ◽  
pp. 13-15
Author(s):  
M. Arunmaran ◽  
K. Kannan
Keyword(s):  
Compact Subset ◽  
Hausdorff Space ◽  
Bitopological Space ◽  
Closed Set ◽  
Continuous Map ◽  
Open Set ◽  
Bitopological Spaces

In this paper, we introduce the concept “Quotient bi-space” in bitopological spaces. In addition, we investigate the results related with quotient bi-space. Moreover, we have discussed the results related with pairwise regular and normal spaces in bitopological space. For a non-empty set X, we can define two topologies (these may be same or distinct topologies) τ1 and τ2 on X. Then, the triple (X, τ1 , τ2 ) is known as bitopological space. Let (X, τ1 , τ2 ) be bitopological space, (Y, σ1 , σ2 ) be trivial bitopological space and f : (X, τ1 , τ2 ) → (Y, σ1 , σ2 ) be onto map. Then f is τ1 τ2 −continuous map. If η = {G (σ − open set in Y ) : f ^{−1} (G) is τ1 τ2 − open in X} then η is a topology on Y . Moreover, if (Y, σ, σ) be a quotient bi-space of (X, τ1 , τ2) under f : (X, τ1 , τ2 ) → (Y, σ, σ) and g : (Y, σ, σ) → (Z, η1 , η2 ) be a map, then, gis σ − continuous if and only if g ◦ f : (X, τ1 , τ2 ) → (Z, η1 , η2 ) is τ1 τ2 −continuous. Let (X, τ1 , τ2) be bitopological space and A be τ1 τ2 − compact subset of pairwise Hausdorff space X. Then, A is τ1 τ2 − closed set. Finally, we have discussed the following : Let (X, τ1 , τ2 ) be bitopological space and τ1 τ2 −compact pairwise Hausdorff space. Then, the space (X, τ1 , τ2 ) is pairwise normal.

scholarly journals Characterizations of Quasi-Metrizable Bitopological Spaces

1988 ◽  
Vol 44 (2) ◽  
pp. 271-274 ◽  
Author(s):  
T. G. Raghavan ◽  
I. L. Reilly
Keyword(s):  
Bitopological Space ◽  
Bitopological Spaces

AbstractIn this paper we prove that a pairwise Hausdorff bitopological space is quasi-metrizable if and only if for each point x ∈ X and for i, j = 1,2, i ≠ j, one can assign nbd bases { S(n, i; x) | n = 1, 2,… } such that (i) y ∉ S (n − 1, i; x) imples S(n, i; x) ∩ S (n, j; y) = φ, (ii) y ∈ S (n, i; x) implies S (n, i; y) ⊂ S(n − 1, i; x). We derive two further results from this.

New forms of separation spaces in bitopology

2016 ◽  
Vol 7 (3) ◽  
pp. 145
Author(s):  
N. Durga Devia ◽  
Raja Rajeswari ◽  
P. Thangavelu
Keyword(s):  
Continuous Function ◽  
Bitopological Space ◽  
Closed Set ◽  
Open Set ◽  
New Type

The aim of this paper is to study how distinct points and a point and a closed set not containing that points are separated by non overlapping open neighborhoods, in a bitopological space. The separation is studied with respect to a new type of \((1,2)\alpha\)-open set together with a continuous function. We named the new axioms as star-ultra \(T_{1}\), star-ultra \(T_{2}\), star-ultra regular and normal. The star-ultra regular spaces is studied in two different ways and are called as A-star-ultra regular and B-star-ultra regular spaces.

On pairwise \(\mathcal{N}\)-\(\beta\)-open sets in bitopological spaces

2016 ◽  
Vol 7 (3) ◽  
pp. 152
Author(s):  
Fahad Alsharari ◽  
Abdo Qahis
Keyword(s):  
Continuous Function ◽  
Open Cover ◽  
Bitopological Space ◽  
Open Set ◽  
Bitopological Spaces

In this paper, we introduce the notion of an \((i,j)\)-\(\mathcal{N}\)-\(\beta\)-open set which is a generalization of an \((i,j)\)-\(\beta\)-open set in a bitopological space. Also, we investigate some of its properties and characterizations. Besides, we prove that a pairwise \((i, j)\)-\(\mathcal{N}\)-\(\beta\)-open cover that has a finite (countable) subcover is equivalent to a pairwise \(\beta\)-compact (\(\beta\)-Lindel\"{ö}f) space. Finally, we introduce an \((i, j)\)-\(\mathcal{N}\)-\(\beta\)-continuous function and an \((i, j)\)-\(\mathcal{N}\)-\(\beta\)-irresolute function and obtain some of their properties.

On regular \beta^-generalized closed set in bitopological space

2016 ◽  
Vol 10 ◽  
pp. 585-591
Author(s):  
Nitin Bhardwaj ◽  
R. S. Verma ◽  
B. P. Garg
Keyword(s):  
Bitopological Space ◽  
Closed Set

scholarly journals Projective bitopological spaces

1972 ◽  
Vol 13 (3) ◽  
pp. 327-334 ◽  
Author(s):  
M. C. Datta
Keyword(s):  
Projective Spaces ◽  
Topological Spaces ◽  
Bitopological Space ◽  
Extremally Disconnected ◽  
Bitopological Spaces

J. C. Kelly [2] introduced the concept of a bitopological space. Lane [3], Patty [4] and Pervin [5] have continued his work. Our purpose in this paper is to identify the projective objects in a suitable category of bitopological spaces after the manner of Gleason [1] and generalize his theorem that in the category of compact Hausdoriff topological spaces, the projective spaces are precisely the extremally disconnected ones.

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