New Types of Almost Countable Dense Homogeneous Space
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, ind...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2010/375293 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549541566480384 |
|---|---|
| author | Abdalla Tallafha Ahmed Al-Rawashdeh |
| author_facet | Abdalla Tallafha Ahmed Al-Rawashdeh |
| author_sort | Abdalla Tallafha |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c9cccd316d464cb6b18b666db681511a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c9cccd316d464cb6b18b666db681511a2025-02-03T06:11:08ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252010-01-01201010.1155/2010/375293375293New Types of Almost Countable Dense Homogeneous SpaceAbdalla Tallafha0Ahmed Al-Rawashdeh1Department of Mathematics, Jordan University, Amman 11942, JordanDepartment of Mathematical Sciences, United Arab Emirates University, Al Ain 15551, UAEIn 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.http://dx.doi.org/10.1155/2010/375293 |
| spellingShingle | Abdalla Tallafha Ahmed Al-Rawashdeh New Types of Almost Countable Dense Homogeneous Space International Journal of Mathematics and Mathematical Sciences |
| title | New Types of Almost Countable Dense Homogeneous Space |
| title_full | New Types of Almost Countable Dense Homogeneous Space |
| title_fullStr | New Types of Almost Countable Dense Homogeneous Space |
| title_full_unstemmed | New Types of Almost Countable Dense Homogeneous Space |
| title_short | New Types of Almost Countable Dense Homogeneous Space |
| title_sort | new types of almost countable dense homogeneous space |
| url | http://dx.doi.org/10.1155/2010/375293 |
| work_keys_str_mv | AT abdallatallafha newtypesofalmostcountabledensehomogeneousspace AT ahmedalrawashdeh newtypesofalmostcountabledensehomogeneousspace |