International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 375293, 11 pages
Research Article

New Types of Almost Countable Dense Homogeneous Space

1Department of Mathematics, Jordan University, Amman 11942, Jordan
2Department of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, UAE

Received 28 September 2009; Revised 19 January 2010; Accepted 9 March 2010

Academic Editor: Richard Wilson

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 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.