Knopp, Paul J.2022-06-222022-06-22197113678560https://hdl.handle.net/10657/9728In this paper, "a locally convex space," or simply "an l.c. space," means "a locally convex, Hausdorff, topological vector space," either real or complex. For an arbitrary l.c. space E[T], necessary and sufficient conditions are found in order for there to exist an l.c. space F[U], a covering of F with bounded subsets of F, and a linear homeomorphism [Phi]:E[T] -> F'[T[lowered G']], where T[lowered G'] is the G'-topology on F' for the pairing <F,F'>...application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital