Copyright © 2010 Abdalla Tallafha and Ahmed Al-Rawashdeh. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In 1972, Bennett studied the countable dense homogeneous (CDH) spaces
and in 1992, Fitzpatrick, White, and Zhou proved that every CDH
space is a space. Afterward Bsoul, Fora, and Tallafha gave another
proof for the same result, also they defined the almost CDH spaces and
almost , spaces, indeed they prove that every ACDH space is an almost space. In this paper we introduce a new type of almost CDH
spaces called ACDH-1, we characterize the ACDH spaces, the almost
spaces, we also give relations between different types of CDH spaces.
We define new type of almost () 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 .