Vol. 46, No. 1, 1973

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A note on countably subparacompact spaces

Thomas Rollin Kramer

Vol. 46 (1973), No. 1, 209–213

It is the purpose of this paper to characterize countably subparacompact spaces in a number of ways and to point out similarities in the pathologies of countably subparacompact spaces and normal spaces. It will be shown inter alia, that a space is countably subparacompact if and only if it is countably a-paracompact, and also if and only if it is countably metacompact and subnormal. The well known product of ordinal spaces, W × W, is shown to be not countably subparacompact, despite the fact that W is compact and W is countably subparacompact and normal.

Mathematical Subject Classification 2000
Primary: 54D20
Received: 25 January 1972
Revised: 15 June 1972
Published: 1 May 1973
Thomas Rollin Kramer