Some Properties of Semi-continuous, Pre-continuous and α-continuous Mappings

This paper investigates some new characteristics of semi-continuous, pre-continuous and α-continuous mappings. We provides two theorems that are equivalent to the definitions of pre-continuous and M-semi-continuous mappings. A condition has been proposed, which makes the injective mapping pre-open. We have proved that the domain of the injective α-continuous mapping with closed graph is Housdorff space. In addition, more other conditions put on the α-continuous mapping, which make its graph closed.