Contra-continuous Maps In Various Of Topological Spaces

Contra-continuity in topological spaces is an important research topic in generaltopology. We study contra-continuous maps in two kinds’topological spaces (i.e., gen-eralized topological spaces and lattice topological spaces), which develops and improvesmap theory in topological spaces. This paper mainly includes the following two aspects:Firstly, it gives the concept of contra-continuous maps in generalized topologicalspaces and illustrates the relationship between contra-continuous maps and continuousmaps in generalized topological spaces. It defines the kernel and frontier in generalizedtopological spaces, and gives the equivalent characterization of contra-continuous mapsin generalized topological spaces. The author finds out the set consist of non-contra-continuous points in generalized topological spaces, conduct a deep research into thenature of contra-continuous maps in generalized topological space, which includes theirprojections, graphs and compositions and so on.Secondly, based on the concept of order homomorphisms in lattice topologicalspaces, it gives the concept of contra-continuous maps in lattice topological spaces andanalyzes their equivalent characterizations. The author conducts a deep research intothe nature of contra-continuous maps in lattice topological spaces, which includes theirprojection, expansion, limitation, composition and so on.