Infinite games and special Baire space extensions

Melven Robert Krom

Vol. 55 (1974), No. 2, 483–487

DOI: 10.2140/pjm.1974.55.483

Abstract

Two known characterizations of Baire spaces, one in terms of open covers and one in terms of infinite games, are proved directly to be equivalent. It is shown that any topological space is a dense subspace of some α-favorable space (a special kind of Baire space) and that any space which is normal and regular (but not necessarily T₁) is a dense subspace of some regular α-favorable space.

Mathematical Subject Classification 2000

Primary: 54E99

Secondary: 02K30

Milestones

Received: 16 July 1974

Revised: 12 September 1974

Published: 1 December 1974