On a question of $C_c(X)$

Commentationes mathematicae Universitatis Carolinae

A. R. Olfati¹ 

关键词: zero-dimensional space;    strongly zero-dimensional space;    $\mathbb{N}$-compact space;    Banaschewski compactification;    character;    ring homomorphism;    functionally countable subring;    functional separability;   

DOI  :  10.14712/1213-7243.2015.161

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

In this short article we answer the question posed in Ghadermazi~M., Karamzadeh O.A.S., Namdari M., {\it On the functionally countable subalgebra of $C(X)$}, Rend. Sem. Mat. Univ. Padova {\bf 129} (2013), 47--69. It is shown that $C_c(X)$ is isomorphic to some ring of continuous functions if and only if $\upsilon_0 X$ is functionally countable. For a strongly zero-dimensional space $X$, this is equivalent to say that $X$ is functionally countable. Hence for every $P$-space it is equivalent to pseudo-$\aleph_0$-compactness.

【 授权许可】

CC BY