Vol. 69, No. 1, 1977

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Noncompact, minimal regular spaces

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

Vol. 69 (1977), No. 1, 19–23

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
Received: 30 April 1976
Revised: 27 October 1976
Published: 1 March 1977
Manuel Phillip Berriozabal
Hon-Fei Lai
Dix Hayes Pettey