Vol. 83, No. 2, 1979

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An anti-open mapping theorem for Fréchet spaces

Steven F. Bellenot

Vol. 83 (1979), No. 2, 325–331
Abstract

It is well-known that completeness is necessary for the usual open mapping theorem for Fréchet spaces. In contrast, it is shown that, with the obvious exception of ω, each infinite-dimensional Fréchet space has another distinct complete topology with the same continuous dual.

Mathematical Subject Classification 2000
Primary: 46A30
Secondary: 46A06
Milestones
Received: 14 July 1978
Revised: 1 March 1979
Published: 1 August 1979
Authors
Steven F. Bellenot