Mapping Theorems On Submeocompact Spaces And Expansive Maps On Non-compact Metric Spaces

In this paper, we discuss the mapping property on submesocompact spaces and expansive maps on non-compact metric spaces.At the first part, we prove that closed Lindelof mappings preserve and inversely preserve submesocompactness on regular spaces, which improves the same result of Lin shou about perfect mappings. We also discuss the mapping property on submesocompact spaces with normal domains.At the second part, We extend the expansive maps on compact metric spaces to non-compact metric spaces. We show that on metric space with Property L, a map f is expansive( positive expansive, non- negative expansive, respectively) if and only if fk is expansive( positive expansive, non- negative expansive, respectively).