On dyadic subspaces

Harold L. Peterson, Jr.

Vol. 31 (1969), No. 3, 773–775

DOI: 10.2140/pjm.1969.31.773

Abstract

We prove a necessary condition for a (compact, Hausdorff) space to be dyadic (= image of product of 2-point spaces):

Theorem. Let Y be a dyadic space of weight m, and let r be a cardinal number less than m. Then X has a dyadic subspace of weight r.

It may be observed (with the aid of Corollary 2, below) that this theorem is a stronger and more general version of a result published in a previous paper by the author [this Journal, 28 (1969), 173–182; Lemma III.6.]

Mathematical Subject Classification

Primary: 54.20

Milestones

Received: 15 April 1969

Published: 1 December 1969