SOME SPECIAL SETS IN AN EXPONENTIAL VECTOR SPACE

In this paper, we have studied `absorbing' and `balanced' sets in an Exponential Vector Space ({\it evs} in short) over the field $\mathbb K$ of real or complex numbers. We have characterised a local base at the additive identity in terms of balanced and absorbing sets in a topological evs over the field $\mathbb K$. We have introduced the concept of `bounded sets' in a topological evs over the field $\mathbb K$ and characterised them with the help of balanced sets. Finally we have introduced the concept of `radial' evs which characterises an evs over the field $\mathbb K$ up to order-isomorphism. It has been shown that ``the usual subspace topology is the finest topology with respect to which $[0,\infty)$ forms a topological evs over the field $\mathbb K$''.