Homogeneity of powers of spaces and the character

Author:

Arhangel’skii A.

Abstract

A space is said to be power-homogeneous if some power of it is homogeneous. We prove that if a Hausdorff space X X of point-countable type is power-homogeneous, then, for every infinite cardinal τ \tau , the set of points at which X X has a base of cardinality not greater than τ \tau , is closed in X X . Every power-homogeneous linearly ordered topological space also has this property. Further, if a linearly ordered space X X of point-countable type is power-homogeneous, then X X is first countable.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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