Regular Wallman compactifications of rim-compact spaces

Journal of the Australian Mathematical Society

Olav Njåstad¹ 

关键词: 54 D 35;   

DOI  :  10.1017/S1446788700019455

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

A compact Hausdorff space is regular Wallman if it possesses a separating ring of regular closed sets, an s-ring. It was proved by P. C. Baayen and J. van Mill [General Topology and Appl. 9 (1978), 125–129] that if a locally compact Hausdorff space possesses an s-ring, then every Hausdorff compactification with zero-dimensional remainder is regular Wallman.In this paper the reasoning leading to this result is modified to work in a more general setting. Iet αX be a Hausdorff compactification of a space X, and letbe the family of those closed sets in αX whose boundaries are contained in X. A main result is the following: Ifcontains an s-ring for some Hausdorff compactification γX, then every larger Hausdorff compactification αX for whichis a base for the closed sets on αX — X, is regular Wallman. Various consequences concerning compactifications of a class of rim-compact spaces (called totally rim-compact spaces) are discussed.

【 授权许可】

Unknown