Barrelled spaces with(out) separable quotients

Authors

  • J. Kakol A. Mickiewicz University
  • S. A. Saxon University of Florida
  • A. R. Todd Baruch College, C.U.N.Y.

Keywords:

barrelled spaces, separable quotients, compact-open topology

Abstract

While the separable quotient problem is famously open for Banach spaces, in the broader context of barrelled spaces we give negative solutions. Obversely, the study of pseudocompact \(X\) and Warner bounded \(X\) allows us to expand Rosenthal's positive solution for Banach spaces of the form \(C_{c}(X)\) to barrelled spaces of the same form, and see that strong duals of arbitrary \(C_{c}(X)\) spaces admit separable quotients. DOI: 10.1017/S0004972714000422

Published

2014-08-03

Issue

Vol. 90 No. 2 (2014)

Section

Articles
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