Vol. 81, No. 2, 1979

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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

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
Received: 4 January 1977
Published: 1 April 1979
Eric Karel van Douwen
Washek (Vaclav) Frantisek Pfeffer