An anti-open mapping theorem for Fréchet spaces

Steven F. Bellenot

Vol. 83 (1979), No. 2, 325–331

DOI: 10.2140/pjm.1979.83.325

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