Properties of Sets in Asymmetric Spaces.

For a space with asymmetric seminorm, the asymmetric closure seminorm is defined as the Minkowski functional of the -closure of the ball . It is shown that an asymmetric normed space is Hausdorff if and only if the closure seminorm is an asymmetric norm on this space. It is also shown that , where . Approximatively compact sets in asymmetric normed -spaces are studied. [ABSTRACT FROM AUTHOR]