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International Journal of Mathematics and Mathematical Sciences
Volume 12, Issue 3, Pages 429-434

*—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 Hindawi Publishing Corporation. 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.


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.