Strong negligibility of σ-compacta does not characterize Hilbert space

Jan Dijkstra

Vol. 127 (1987), No. 1, 19–30

DOI: 10.2140/pjm.1987.127.19

Abstract

It is proved that the complement X of a σZ-set in a Q-manifold is an l²-manifold if every finite dimensional compactum is strongly negligible in X. Moreover, we show that this statement is false in the general setting: there exists a complete AR in which every σ-compactum is strongly negligible but which does not satisfy the discrete 2-cells property.

Mathematical Subject Classification 2000

Primary: 57N20

Secondary: 46C05

Milestones

Received: 7 October 1985

Published: 1 March 1987