Birelator Spaces Are Natural Generalizations of Not Only Bitopological Spaces, But Also Ideal Topological Spaces

2019 ◽  
pp. 543-586
Author(s):  
Árpád Száz
Keyword(s):  
Topological Spaces ◽  
Bitopological Spaces

PAIRWISE α-PARACOMPACT SUBSETS

2021 ◽  
Vol 10 (5) ◽  
pp. 2631-2639
Author(s):  
M. Benbettiche ◽  
H.Z. Hdeib
Keyword(s):  
Topological Spaces ◽  
Definition Of ◽  
Bitopological Spaces

In this paper we define pairwise-$\alpha$-paracompact subsets as a generalisation of $\alpha$-paracompact subsets in topological spaces and study their properties and its relations with other bitopological spaces. Several theorems are obtained concerning pairwise-$\alpha$-paracompact sets. We introduced the definition of $p$-paracompact bitoplogical spaces and study their properties and its relations with other bitopological spaces.

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.

scholarly journals Some Results of τ1τ2-δ Semiconnectedness and Compactness in Bitopological Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-4
Author(s):  
M. Arunmaran ◽  
K. Kannan
Keyword(s):  
Topological Spaces ◽  
Bitopological Space ◽  
Bitopological Spaces ◽  
The Relationship

We are going to establish some results of τ1τ2-δ semiconnectedness and compactness in a bitopological space. Besides, we will investigate several results in τ1τ2-δ semiconnectedness for subsets in bitopological spaces. In particular, we will discuss the relationship related to semiconnectedness between the topological spaces and bitopological space. That is, if a bitopological space (X,τ1,τ2) is τ1τ2-δ semiconnected, then the topological spaces (X,τ1) and (X,τ2) are δ-semiconnected. In addition, we introduce the result which states that a bitopological space (X,τ1,τ2) is τ1τ2-δ semiconnected if and only if X and ϕ are the only subsets of X which are τ1τ2-δ semiclopen sets. Moreover, we have proved some results in compactness also. Altogether, several results of τ1τ2-δ semiconnectedness and compactness in a bitopological space have been discussed.

scholarly journals On T1 T2-g-Open Sets in Bitopological Spaces

2019 ◽  
pp. 1-8
Author(s):  
K. Vithyasangaran ◽  
P. Elango ◽  
S. Sathaananthan ◽  
J. Sriranganesan ◽  
P. Paramadevan
Keyword(s):  
Continuous Function ◽  
Topological Spaces ◽  
Bitopological Space ◽  
Open Set ◽  
Bitopological Spaces

In this paper, we introduced and studied a new kind of generalized open set called τ1τ2-g-open set in a bitopological space (X, τ1, τ2). The properties of this τ1τ2-g-open set are studied and compared with some of the corresponding generalized open sets in general topological spaces and bitopological spaces. We also dened the τ1τ2-g-continuous function and studied some its properties.

scholarly journals Level Separation on Fuzzy Pairwise T0bitopological Space

2017 ◽  
Vol 41 (1) ◽  
pp. 57-68
Author(s):  
MS Hossain ◽  
Ummey Habiba
Keyword(s):  
Extension Property ◽  
Topological Spaces ◽  
Fuzzy Topological Spaces ◽  
Academy Of Sciences ◽  
Bitopological Spaces

In this paper, we introduce five notions of level separation in T0 fuzzy bitopological spaces. We establish some relation among them. Also, we find relations between fuzzy topological spaces and corresponding fuzzy bitopological spaces in such spaces. Further, we prove that all these definitions satisfy “good extension” property. Finally, we prove that all these notionsare hereditary, productive and projective, moreover we observe that all concepts are preserved under one-one, onto and continuous mapping.Journal of Bangladesh Academy of Sciences, Vol. 41, No. 1, 57-68, 2017

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 Characterization of Soft S-Open Sets in Bi-Soft Topological Structure Concerning Crisp Points

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2100
Author(s):  
Arif Mehmood ◽  
Mohammed M. Al-Shomrani ◽  
Muhammad Asad Zaighum ◽  
Saleem Abdullah
Keyword(s):  
Coordinate Space ◽  
Regular Space ◽  
Topological Spaces ◽  
Finite Intersection ◽  
Open Set ◽  
Separation Axioms ◽  
Finite Intersection Property ◽  
Almost All ◽  
Bitopological Spaces

In this article, a soft s-open set in soft bitopological structures is introduced. With the help of this newly defined soft s-open set, soft separation axioms are regenerated in soft bitopological structures with respect to crisp points. Soft continuity at some certain points, soft bases, soft subbase, soft homeomorphism, soft first-countable and soft second-countable, soft connected, soft disconnected and soft locally connected spaces are defined with respect to crisp points under s-open sets in soft bitopological spaces. The product of two soft  axioms with respect crisp points with almost all possibilities in soft bitopological spaces relative to semiopen sets are introduced. In addition to this, soft (countability, base, subbase, finite intersection property, continuity) are addressed with respect to semiopen sets in soft bitopological spaces. Product of soft first and second coordinate spaces are addressed with respect to semiopen sets in soft bitopological spaces. The characterization of soft separation axioms with soft connectedness is addressed with respect to semiopen sets in soft bitopological spaces. In addition to this, the product of two soft topological spaces is (  space if each coordinate space is soft  space, product of two sot topological spaces is (S regular and C regular) space if each coordinate space is (S regular and C regular), the product of two soft topological spaces is connected if each coordinate space is soft connected and the product of two soft topological spaces is (first-countable, second-countable) if each coordinate space is (first countable, second-countable).

scholarly journals Si-open sets ans Si-continuity in bitopological spaces

2012 ◽  
Vol 43 (1) ◽  
pp. 81-97
Author(s):  
Alias Barakat Khalaf
Keyword(s):  
Topological Spaces ◽  
New Class ◽  
Bitopological Spaces

In this paper we introduce and de ne a new class of sets, called Si-open sets,in bitopological spaces. By using this set we introduce the notion of Si-continuity and investigate some of its properties. In particular, Si-open sets and Si-continuity are used to extend some known results in topological spaces.

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 A Note on Some Generalized Closed Sets in Bitopological Spaces Associated to Digraphs

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
K. Kannan
Keyword(s):  
Graph Theory ◽  
Short Communication ◽  
Topological Spaces ◽  
Closed Sets ◽  
Bitopological Spaces ◽  
The Relationship

Many investigations are undergoing of the relationship between topological spaces and graph theory. The aim of this short communication is to study the nature and properties of some generalized closed sets in the bitopological spaces associated to the digraph. In particular, some relations between generalized closed sets in the bitopological spaces associated to the digraph are characterized.

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