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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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Take to be – semicompact. The discussion in the comments to Brian M.

Subscribe to Table of Contents Alerts. In particular, we will discuss the relationship related to semiconnectedness between the topological spaces and bitopological space. A nonempty collection is called a – semiopen cover of a bitopological spaceif and – – and contains at least one member of – and one member of.

Thus, is – semiconnected. I don’t know where they occur, but now they can get married here in NYC: The book Bitopological Spaces: I would also like to know where bitopological spaces have some applications in various parts in mathematics. Let be subset of bitopological bito;ological. We are going to establish some results of – semiconnectedness and compactness in a bitopological space.


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Bitopological space

Since is – semiclosed, is – semiopen. Now there exist such that also since and also and sincewhich shows that is – semidisconnected subset and biitopological is a contradiction. Then, is called – semiopen set, if there exists an – open set such that -cl. Then the triple is called a bitopological space. Perhaps it’s worth mentioning that this condition also appears in some papers on quasi-metric spaces.

Since is – semicompact. So we are interested to check whether those results will work for bitopological space or not. Suppose is – semiconnected. Let – int and – cl are the -interior and -closure of with respect to the topologyrespectively,where and are semiregularization of andrespectively. Partial Differential Equations 22 1 73— Then zpaces be expressed as the union of two nonempty disjoint sets and such that – – Also is – semiopen and is – semiopen.


Most users should sign in with their email address. Moreover, we have presented some results of – semiconnectedness in bitopological spaces in [ 8 ]. Sign In or Create an Account.

spacex Related articles in Google Scholar. Definition 6 see [ 6 ]. Mathematics Stack Exchange works best with JavaScript enabled. If the results fail to hold for bitopology, we are going to illustrate by examples.

Gradient flows in asymmetric metric spaces Nonlinear Analysis: Now, assume that is not – semiconnected. Sign up using Email and Password.

Patty : Bitopological spaces

If is – semiclosed subset of a – semicompact space then is – semicompact. Complement of – open set is called – closed slaces 2 is said to be – open set, if forthere exists -regular open set such that. If a bitopological space is – semiconnected, then is – semiconnected.