ON SD-CONNECTED SPACES

In this article, we introduce a stronger form of connected space using the notion of somewhere dense sets, namely SD-connected space. Firstly, we define SDseparated sets in topological spaces,then we discuss their characterizationsand use their notions to study the behaviour of SD-connected space. Moreover, we discuss the concept of SD-connected sets and SD-connected subspaces, where we show that these concepts are different. Additionally, images of SDconnected space are established under some particular maps as SD-irresolute maps and SD-continuous maps. Finally, we prove that any somewhere dense set is dense inSD-connected space, also we illustrate the relationships between this class of spaces and strongly hyperconnected space, hyperconnected space and connected space, and we show that these spaces are strongly ordered as: strongly hyperconnected space, SD-connected space, hyperconnected space and then connected space.