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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Email Required, but never shown. In this paper, we have used the result that every – closed set is – semiclosed.

Journal of Mathematics

Definition 6 see [ 6 ]. They are defined as metric spaces, but the symmetry in the definition of metric is omitted. Two valued measure and summability of double sequences in asymmetric contextActa Mathematica Hungarica, 1—2— and without any name in J. Close mobile search navigation Article navigation.

Complement of – open set is called – closed set.

Patty : Bitopological spaces

Indexed in Web of Science. In particular, we will discuss the relationship related to semiconnectedness between the topological spaces and bitopological space. Dvalishvili, Tbilisi, Georgia elsevier. Then cannot be expressed as the union of two nonempty disjoint sets and such that – – Also bitopologixal – semiopen and is – semiopen.


In this paper, some results of – semiconnectedness and compactness in bitopological spaces have been discussed. This article is also spsces for rental through DeepDyve. Suppose that is not – semiconnected. Sincewe have.

Then is also – semiconnected. Kannan, Department of Mathematics and Statistics, University of Jaffna, Sri Lanka, for providing important references from the literature. Scott’s answer here motivated me to ask about bitopological spaces. Simultaneously, the bitopological spaces have several applications in analysis, general topology, and theory of ordered topological spaces.


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. Therefore, is – semiconnected. If is – closed subset of a – semicompact space then is – semicompact.

bitopological space in nLab

Then is called -open, if. Nitopological my opinion, if some slaces which hold in these setting could be stated and proven in a unifying way using bitopological spaces such that one of the topologies is finer than the other one, I would personally prefer such formulation even in a paper which deals with only one of these settings.


By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Sign In or Create an Account. Article PDF first page preview. View at Google Scholar T. So and are -semiconnected spaces. Moreover, we have proved some results in compactness also. Then, 1 is said to be – open set, if, for bihopological, there exists -regular open set such that. Do they have applications?

View at Scopus K. If is – semiclosed subset of a – semicompact space then is – semicompact. Let be subset of a bitopological space. Elimination of cusps in dimension 4 and its applications.

This contradicts our supposition. Consider a – semiconnected space ; let biropological is – semiclopen set; then is – semidisconnected in the bitopological space, which is contradiction. Similarly, we can prove .