Some special sets in an exponential vector space. (English) Zbl 1488.46018
Summary: In this paper, we have studied ‘absorbing’ and ‘balanced’ sets in an Exponential Vector Space (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 \(\mathbb K\)”.
Keywords:
topological exponential vector space; order-isomorphism; absorbing set; balanced set; bounded set; radial evsReferences:
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