In this paper, we introduce a new type of closed sets in bitopological space (X, τ1, τ2), used it to construct new types of normality, and introduce new forms of. Definitions. Recall that a topological space is a set equipped with a topological structure. Well, a bitopological space is simply a set equipped. Citation. Patty, C. W. Bitopological spaces. Duke Math. J. 34 (), no. 3, doi/S

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But this is not true for bitopological space in general.

View at Google Scholar A. Let – int and – cl are the -interior and -closure of with respect to the topologyrespectively,where and are semiregularization of and spafes, respectively.

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Since every – open set and – open set are – semiopen set and – semiopen set, respectively, So if and are -semidisconnected spaces then the bitopological space becomes -semidisconnected. Such spaces naturally bear two topologies: He introduced this concept in his journal of London Mathematical Society in Email Required, but never shown.

Proposition 14 see [ 8 ]. Since is – semicompact. Sign up using Email and Password.


The union of any family of – semiconnected sets with a nonempty intersection is – semiconnected. Suppose can be so expressed, then is called – semidisconnected space and we write and it is called – semiseparation of.

Since every – open set is – semiopen, we have and – – and contains at least one member of – and one member of. This article is bitopologicwl available for rental through DeepDyve. A bitopological space is called – compact, if every – open cover of has a finite subcover. Simultaneously, the bitopological spaces have several applications in analysis, general topology, and theory of ordered topological spaces.

In addition, we introduce the result which states that a bitopological space is – semiconnected if and only if and are the only subsets of which are – semiclopen sets. Most spacea should sign in with their email address. Related articles in Google Scholar. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Since every – closed set is – semiclosed, is – semiclosed.

Bitopological Spaces | Proceedings of the London Mathematical Society | Oxford Academic

Assume that can be expressed as the union of two nonempty disjoint sets and such that is – semiopen and is – semiopen, respectively. In this paper, some results of – semiconnectedness and compactness in bitopological spaces have been discussed. Altogether, several results of – semiconnectedness and compactness in a bitopological space have been discussed. Character formulas and Bernstein—Gelfand—Gelfand resolutions for Cherednik algebra modules. Facebook Twitter Advertising and Corporate Services.


Mielke, Existence results for energetic models for rate-independent systems, Calc. The book Bitopological Spaces: A related question was posted at MO: Thus, is – semicompact. Dvalishvili, Tbilisi, Georgia elsevier. Takewhere each is – semiconnected with.

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View at Google Scholar F. Then is called 1 -regular open, if -int -cl ; 2 -regular open, if -int -cl ; 3 -semiopen, if -cl -int ; 4 -semiclosed, if -int -cl Definition bitopoogical see [ 9 ]. I am not sure to which extent my background is important, but I never studied bitopological spaces, although I have read two papers on quasi-metric spaceswhich are a special case.