Connectednesses And Disconnectednesses Of Bi-pre-topological Spaces

Using topological and categorial methods, connectednesses and disconnectednesses of bi-pre-topological spaces are deeply studied, and some good properties are obtained. At last, take the disconnectednesses for example, the struc-ture of some special disconnectednesses of bi-pre-topological spaces are discussed in detail.The main contents are as follows:Chapter one:Preliminary knowledge, in this chapter, we will give the basic concepts and results of the theory of bi-pre-pretopological space and that of category which are used in the whole paper.Chapter two:A category theorem of bi-pre-topological space. Using the way of category, the category of bi-pre-topological spaces are proved to be a topological construct.Chapter three:Connectednesses and disconnectednesses of bi-pre-topological spaces. Firstly,connectednesses and disconnectednesses of bi-pre-topological spaces are introduced, and a characterization of connectednesses and disconnectednesses of bi-pre-topological spaces are given. Secondly;the properties of continuously closed, productive and mono-hereditary of connectednesses and disconnectednesses of bi-pre-topological spaces are proved. Finally, close connections between pre-topological spaces and bi-pre-topological spaces of connectednesses and disconnectednesses are established.Chapter four:The structure of special disconnectednesses of bi-pre-topological spaces. The structure of some disconnectednesses of bi-pre-topological spaces N which including two-element are discussed...