Some properties of the Sorgenfrey line and related spaces

Eric Karel van Douwen and Washek (Vaclav) Frantisek Pfeffer

Vol. 81 (1979), No. 2, 371–377

DOI: 10.2140/pjm.1979.81.371

Abstract

Any finite power Sⁿ of the Sorgenfrey line S has this covering property: if φ(x) is a neighborhood of x for each x ∈ Sⁿ, then there is a closed discrete subset D of Sⁿ such that {φ(x) : x ∈ D} covers Sⁿ. No finite power of the Sorgenfrey line is homeomorphic to finite power of the irrational Sorgenfrey line. The Sorgenfrey plane is not the union of countably many nice subspaces.

Mathematical Subject Classification 2000

Primary: 54D20

Secondary: 54F05

Milestones

Received: 4 January 1977

Published: 1 April 1979