期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：2010
卷号：2010
DOI：10.1155/2010/375293
出版社：Hindawi Publishing Corporation
摘要：In 1972, Bennett studied the countable dense homogeneous (CDH) spaces
and in 1992, Fitzpatrick, White, and Zhou proved that every CDH
space is a 𝑇1 space. Afterward Bsoul, Fora, and Tallafha gave another
proof for the same result, also they defined the almost CDH spaces and
almost 𝑇1, 𝑇0 spaces, indeed they prove that every ACDH space is an almost 𝑇1 space. In this paper we introduce a new type of almost CDH
spaces called ACDH-1, we characterize the ACDH spaces, the almost
𝑇0 spaces, we also give relations between different types of CDH spaces.
We define new type of almost 𝑇1 (𝐴𝑇1) spaces, and we study the relations between the old and new definitions. By extending the techniques
given by Tallafha, Bsoul, and Fora, we prove that every ACDH-1 is an 𝐴𝑇1.
