Pseudouniform topologies on $C(X)$ given by ideals

Commentationes mathematicae Universitatis Carolinae

Roberto Pichardo-Mendoza¹ 

关键词: function space;    topology of uniform convergence;    ideal;    uniformity;    Lindel\"of property;    pseudouniform ideal;    almost pseudo-$\omega$-bounded;   

DOI  :  

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 】

Given a Tychonoff space $X$, a base $\alpha$ for an ideal on $X$ is called {\it pseudouniform\/} if any sequence of real-valued continuous functions which converges in the topology of uniform convergence on $\alpha$ converges uniformly to the same limit. This paper focuses on pseudouniform bases for ideals with particular emphasis on the ideal of compact subsets and the ideal of all countable subsets of the ground space.

【 授权许可】

CC BY