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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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Facebook Twitter Advertising and Corporate Services. So, is – semiconnected. Further, we want to find how uniform continuity will work in bitopological spaces. Bitopological spaces and algebraic topology.

Journal of Mathematics

Thus, is – semicompact. Progress in Mathematics, vol. Assume that can be expressed as the union of two nonempty disjoint sets bitopoloigcal such that is – semiopen and is – semiopen, respectively. You could not be signed in. Abstract We are going to establish some results of – semiconnectedness and compactness in a bitopological space.

Let be family of – semiconnected subsets of a bitopological space such ibtopological ; then is also – semiconnected. Scott’s answer here motivated me to ask about bitopological spaces.


The union of any family of – semiconnected sets with a nonempty intersection is – semiconnected. So and ; then and both are – semiclopen sets and each of them is neither nor.

Recently, Edward Samuel and Balan [ 6 ] established the concept – semiopen sets in bitopological spaces.

Bitopological space – Wikipedia

Definition 6 see [ 6 ]. Sign up or log in Sign up using Google. Then, is called – semiopen set, if there exists an – open set such that -cl. A quasimetric on a set is a nonnegative real valued function on the Cartesian product of that satisfies the following three axioms: Suppose that is not – semiconnected. Then by applying Proposition 20is – semicompact.

Article PDF first page preview. The concept semiconnectedness and compactness is used in various parts of Mathematics.

Since every – open set is – semiopen, we have and – – bitopopogical contains at least one member of – and one member of. Semiconnectedness Proposition 12 see [ 8 ].

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Take to be – semicompact. We already had a discussion about quasi-metrics here. Maheshwari spacws Prasad [ 2 ] introduced semiopen sets in bitopological spaces in Since is – semiconnected andwe have or. Sign up using Facebook. This contradicts our supposition.


Some Results of – Semiconnectedness and Compactness in Bitopological Spaces

And be a – semiopen cover of. Let cannot be expressed as the union of two nonempty sets with such that is – semiopen and is – semiopen. Definition 2 see [ 1 ]. Inthe notion -open sets in bitopological spaces was introduced by Banerjee [ 3 ]. Sign In Forgot password?

Conflicts of Interest The authors declare that they have no conflicts of interest. If cannot be expressed as the union of two disjoint sets and such that is – semiopen and is – semiopen, then does not contain any nonempty proper subset which is both – semiopen and – semiclosed.