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- W2034228912 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<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>T</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>space. Afterward Bsoul, Fora, and Tallafha gave another proof for the same result, also they defined the almost CDH spaces and almost<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>T</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>,<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>T</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>spaces, indeed they prove that every ACDH space is an almost<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>T</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>space. In this paper we introduce a new type of almost CDH spaces called ACDH-1, we characterize the ACDH spaces, the almost<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>T</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math>spaces, we also give relations between different types of CDH spaces. We define new type of almost<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>T</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>(<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>AT</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>) 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<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msub><mml:mi>AT</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:math>." @default.
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- W2034228912 date "2010-01-01" @default.
- W2034228912 modified "2023-09-24" @default.
- W2034228912 title "New Types of Almost Countable Dense Homogeneous Space" @default.
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- W2034228912 doi "https://doi.org/10.1155/2010/375293" @default.
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