ON VECTOR SPACES WITH LOCALLY BOUNDED CONVERGENCE STRUCTURES

Abstract

It is known that a precompact set in a limit vector space is not necessarily bounded. In this paper it is shown that the topological vector space result that every precompact set is bounded can be extended to the large class of locally bounded prelimit vector spaces. This result is used to extend the well-known characterization of finite-dimensional separated topological vector spaces to locally bounded prelimit vector spaces.