Semicontinuity, Semiconnected and Semicompactness in Bitopological Spaces

Abstract

Let \(\tau_{1}\) and \(\tau_{2}\) be two topologies(same or distinct) which are defined in a nonempty set \(X\). Then, the triple \((X,\tau_{1},\tau_{2})\) is called as a bitopological space. The objective of this paper is to establish some results which are related with semi compactness in bitopological spaces and discuss the relationships between semi continuous function in bitopological space and various topological spaces. In particular, we identify the relationship between the bitopological spaces and their product space in semi compactness. Throughout this paper, we are able to get the clear understanding about the concept `semi compactness' and how to connect this concept with topological spaces and bitopological space. In addition, we can identify how to connect the continuous maps and product spaces with semi compactness. In addition, we can identify the relationships between semi continuous function in bitopological space and various topological spaces.