Noncompact, minimal regular spaces

Manuel Phillip Berriozabal, Hon-Fei Lai and Dix Hayes Pettey

Vol. 69 (1977), No. 1, 19–23

DOI: 10.2140/pjm.1977.69.19

Abstract

In the first known example of a noncompact, minimal regular space, the standard Tychonoff plank is used in the construction. In the present paper, this construction is generalized by using, instead of the standard Tychonoff plank, a generalized Tychonoff plank which is defined in terms of an arbitrary pair of ordinals. Such a construction yields a noncompact, minimal regular space if and only if both ordinals are limit ordinals and at least one of them is uncountably cofinal.

Mathematical Subject Classification 2000

Primary: 54D15

Milestones

Received: 30 April 1976

Revised: 27 October 1976

Published: 1 March 1977