Vol. 51, No. 2, 1974

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Two properties of the Sorgenfrey plane

William George Bade

Vol. 51 (1974), No. 2, 349–354

The Sorgenfrey line S is the real line with the topology generated by the half open intervals [a,b). R. H. Sorgenfrey proved that S is paracompact, while S × S is not paracompact, or even normal. The two main results of this paper are that S × S is strongly zero-dimensional, and that every real continuous function on S ×S in the first Baire class for the Euclidean topology of the plane. These results answer questions asked by P. Nyikos.

Mathematical Subject Classification 2000
Primary: 54F45
Secondary: 54G20
Received: 13 January 1972
Revised: 1 November 1973
Published: 1 April 1974
William George Bade