TY - JOUR

T1 - New types of almost countable dense homogeneous space

AU - Tallafha, Abdalla

AU - Al-Rawashdeh, Ahmed

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

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U2 - 10.1155/2010/375293

DO - 10.1155/2010/375293

M3 - Article

AN - SCOPUS:77952577944

VL - 2010

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

SN - 0161-1712

M1 - 375293

ER -