几乎第二可数空间、几乎第一可数空间和几乎可分空间(英文)

Almost Second Countable Spaces, Almost First Countable Spaces and Almost Separable Spaces

本文定义了几乎第二可数空间,几乎第一数可空间和几乎可分空间,它们分别是第二可数空间,第一可数空间和可分空间的一般化,还研究了这三类新空间以及几乎Lindelof空间的性质,改进了[2]中的几个定理.

In this paper, we introduce almost second countable spaces, almost first countable spaces and almost separable spaces which are generalisations of second countable, first countable and separable spaces, respectively. We also study the prop-erties of the three new classes of spaces and almost Lindelof spaces and improve some results in [2].