Characterizations of some C^∗-embedded subspaces of βN

R. Grant Woods

Vol. 65 (1976), No. 2, 573–579

DOI: 10.2140/pjm.1976.65.573

Abstract

Let K be a compact F-space such that |C^∗(K)| = 2^ω. Using the continuum hypothesis we characterize those subspaces of K that are C^∗-embedded in K. We also characterize the class of extremally disconnected Tychonoff spaces of countable cellularity. As corollaries of these theorems, using various set-theoretic hypotheses we characterize the C^∗-embedded, and the extremally disconnected C^∗-embedded, subspaces of βN.

Mathematical Subject Classification 2000

Primary: 54D35

Secondary: 54C45

Milestones

Received: 7 January 1976

Revised: 12 April 1976

Published: 1 August 1976