Two properties of the Sorgenfrey plane

William George Bade

Vol. 51 (1974), No. 2, 349–354

DOI: 10.2140/pjm.1974.51.349

Abstract

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

Milestones

Received: 13 January 1972

Revised: 1 November 1973

Published: 1 April 1974