Zero-set ultrafilters and Gδ-closures in uniform spaces

Journal of the Australian Mathematical Society

Howard Curzer¹ 

[1] Anthony W. Hager

关键词: uniform space;    metric-fine space;    zero-set;    ultrafilter;    Gδ-closure;    realcompact;    topologically complete;    KatÄ›tov-Shirota;    epi-reflective.;   

DOI  :  10.1017/S1446788700015718

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

The paper examines the classes K1 and Γ1 of Hausdorff uniform spaces which are Gδ-closed in their Samuel compactifications, or completions. It is shown that the classes are epi-reflective, the reflections K1 and Γ are described, K1 and Γ1 are represented as epi-reflective hulls, membership in the classes is described by fixation of certain zero-set ultrafilters, and it is shown that k1 = Γ1 exactly on spaces without discrete sets of measurable power. The results include familiar facts about realcompact and topologically complete topological spaces and are closely connected with the theory of metric-fine uniform spaces.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 54 C 50, 54 E 15, 18 A 40; secondary 54 B 05, 54 B 10, 54 C 10, 54 C 30.

【 授权许可】

Unknown