Another note on Eberlein compacts

Ernest A. Michael and Mary Ellen Rudin

Vol. 72 (1977), No. 2, 497–499

DOI: 10.2140/pjm.1977.72.497

Abstract

An Eberlein compact is a compact space that can be embedded in a Banach space with its weak topology. It is shown that: If X is compact and if X = M₁ ∪M₂ with M₁ and M₂ metrizable, then M₁ ∩M₂ is metrizable and X is an Eberlein compact. This answers a question of Arhangel’skiǐ.

Mathematical Subject Classification 2000

Primary: 54C25

Secondary: 46B99

Milestones

Received: 20 May 1977

Published: 1 October 1977