Some Properties of Semi-continuous, Pre-continuous and α-continuous Mappings |
( Volume 2 Issue 5,May 2015 ) OPEN ACCESS |
Author(s): |
Yasser A. Abou-Elwan |
Abstract: |
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.
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