International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 3, Pages 429-434
doi:10.1155/S0161171289000529
*—Inductive limits and partition of unity
Department of Mathematics, Rhodes University, Grahamstown 6140, South Africa
Received 16 November 1987; Revised 22 September 1988
Copyright © 1989 V. Murali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In this note we define and discuss some properties of partition of unity on
*-inductive limits of topological vector spaces. We prove that if a partition of unity exists
on a *-inductive limit space of a collection of topological vector spaces, then it is
isomorphic and homeomorphic to a subspace of a *-direct sum of topological vector spaces.