Publication Date:
2010-01-01
Description:
In 1972, Bennett studied the countable dense homogeneous (CDH) spaces and in 1992, Fitzpatrick, White, and Zhou proved that every CDH space is aT1space. Afterward Bsoul, Fora, and Tallafha gave another proof for the same result, also they defined the almost CDH spaces and almostT1,T0spaces, indeed they prove that every ACDH space is an almostT1space. In this paper we introduce a new type of almost CDH spaces called ACDH-1, we characterize the ACDH spaces, the almostT0spaces, we also give relations between different types of CDH spaces. We define new type of almostT1(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 anAT1.
Print ISSN:
0161-1712
Electronic ISSN:
1687-0425
Topics:
Mathematics
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