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New Types of Almost Countable Dense Homogeneous Space

Author

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  • Abdalla Tallafha
  • Ahmed Al-Rawashdeh

Abstract

In 1972, Bennett studied the countable dense homogeneous (CDH) spaces and in 1992, Fitzpatrick, White, and Zhou proved that every CDH space is a 𠑇 1 space. Afterward Bsoul, Fora, and Tallafha gave another proof for the same result, also they defined the almost CDH spaces and almost 𠑇 1 , 𠑇 0 spaces, indeed they prove that every ACDH space is an almost 𠑇 1 space. In this paper we introduce a new type of almost CDH spaces called ACDH-1, we characterize the ACDH spaces, the almost 𠑇 0 spaces, we also give relations between different types of CDH spaces. We define new type of almost 𠑇 1 ( ð ´ ð ‘‡ 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 ð ´ ð ‘‡ 1 .

Suggested Citation

  • Abdalla Tallafha & Ahmed Al-Rawashdeh, 2010. "New Types of Almost Countable Dense Homogeneous Space," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-11, May.
    • Handle: RePEc:hin:jijmms:375293
    DOI: 10.1155/2010/375293
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