Glasnik Matematicki, Vol. 34, No.1 (1999), 65-72.

PROPER METRIC SPACES AND HIGSON COMPACTIFICATIONS OF PRODUCT SPACES

Kazuo Tomoyasu

Abstract.   Let (X, d) be a non-compact metric space. We provide an equivalent condition that the metric d is proper on X. X^d denotes the Higson compastification of a non-compact proper metric space (X, d). In this paper we show that if (X, d_X) is a non-compact proper metric space and (Y, d_Y) is a non-compact metric space, then X × Y ^{max{dX, dY}} is not equivalent to X ^dX × Y ^dY.

1991 Mathematics Subject Classification.   54D35, 54D40.

Key words and phrases.   Higson compactification, Higson corona, proper metric spaces.