Almost separable spaces

[摘要] In this article, we introduce the notion of almost separable space, which is a generalization of separable space. We show that like separability, almost separability is $c$-productive and the converse is true under some restrictions. We discuss about the cardinality of the set of all real valued continuous functions on an almost separable space. Finally, we establish a Baire Category Like theorem on pseudocompact space.

[学科分类] 公共、环境与职业健康

[关键词] Almost separable space;Pseudocompact space;Functionally Hausdorff space;Sequentially separable space;Strongly sequentially separable space