In 1972, Bennett studied the countable dense homogeneous (CDH) spaces and in 1992, Fitzpatrick, White, and Zhou proved that every CDH space is a T 1 space. Afterward Bsoul, Fora, and Tallafha gave another proof for the same result, also they defined the almost CDH spaces and almost T 1, T 0 spaces, indeed they prove that every ACDH space is an almost T 1 space. In this paper we introduce a new type of almost CDH spaces called ACDH-1, we characterize the ACDH spaces, the almost T 0 spaces, we also give relations between different types of CDH spaces. We define new type of almost T 1 (AT 1) 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 AT 1.
|Journal||International Journal of Mathematics and Mathematical Sciences|
|Publication status||Published - 2010|
ASJC Scopus subject areas
- Mathematics (miscellaneous)