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 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 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.

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 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.

scholarly journals On pairwise paracompactness

1992 ◽  
Vol 53 (2) ◽  
pp. 281-285 ◽  
Author(s):  
M. Ganster ◽  
I. L. Reilly
Keyword(s):  
Open Cover ◽  
The Other ◽  
Bitopological Space ◽  
Locally Finite ◽  
Other Hand ◽  
Bitopological Spaces ◽  
The Relationship

AbstractThis paper answers a recent question concerning the relationship between two notions of paracompactness for bitopological spaces. Romaguera and Marin defined pairwise paracompactness in terms of pair open covers, motivated by a characterization of paracompactness due to Junnila. On the other hand, Raghavan and Reilly defined a bitopological space (X, τ, σ) to be δ-pairwise paracompact if and only if every τ open (σ open) cover of X admits a τ V σ open refinement which is τ V σ locally finite. It is shown that pairwise paracompactness implies δ-pairwise paracompactness, and that the converse is false.

scholarly journals Some Modifications of Pairwise Soft Sets and Some of Their Related Concepts

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1781
Author(s):  
Samer Al Ghour
Keyword(s):  
Topological Space ◽  
Sufficient Conditions ◽  
Soft Sets ◽  
New Concepts ◽  
Bitopological Spaces ◽  
The Relationship ◽  
Soft Topological Space

In this paper, we first define soft u-open sets and soft s-open as two new classes of soft sets on soft bitopological spaces. We show that the class of soft p-open sets lies strictly between these classes, and we give several sufficient conditions for the equivalence between soft p-open sets and each of the soft u-open sets and soft s-open sets, respectively. In addition to these, we introduce the soft u-ω-open, soft p-ω-open, and soft s-ω-open sets as three new classes of soft sets in soft bitopological spaces, which contain soft u-open sets, soft p-open sets, and soft s-open sets, respectively. Via soft u-open sets, we define two notions of Lindelöfeness in SBTSs. We discuss the relationship between these two notions, and we characterize them via other types of soft sets. We define several types of soft local countability in soft bitopological spaces. We discuss relationships between them, and via some of them, we give two results related to the discrete soft topological space. According to our new concepts, the study deals with the correspondence between soft bitopological spaces and their generated bitopological spaces.

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.

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