Uniform topology on EQ-algebras
In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, 𝓚), and then the part 𝓚 induce a uniform topology 𝒯 in E. We prove that the pair (E, 𝒯) is a topological EQ-algebra, and some properties of (E, 𝒯) are investigated. In particular, we show that (E, 𝒯) is a first-counta...
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| Format: | Article |
| Language: | English |
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De Gruyter
2017-04-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0032/math-2017-0032.xml?format=INT |
| _version_ | 1818057891280584704 |
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| author | Yang Jiang Long Xin Xiao He Peng Fei |
| author_facet | Yang Jiang Long Xin Xiao He Peng Fei |
| author_sort | Yang Jiang |
| collection | DOAJ |
| description | In this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, 𝓚), and then the part 𝓚 induce a uniform topology 𝒯 in E. We prove that the pair (E, 𝒯) is a topological EQ-algebra, and some properties of (E, 𝒯) are investigated. In particular, we show that (E, 𝒯) is a first-countable, zero-dimensional, disconnected and completely regular space. Finally, by using convergence of nets, the convergence of topological EQ-algebras is obtained. |
| first_indexed | 2024-12-10T12:51:56Z |
| format | Article |
| id | doaj.art-04176da47e504750803e669d31e519d2 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-10T12:51:56Z |
| publishDate | 2017-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-04176da47e504750803e669d31e519d22022-12-22T01:48:11ZengDe GruyterOpen Mathematics2391-54552017-04-0115135436410.1515/math-2017-0032math-2017-0032Uniform topology on EQ-algebrasYang Jiang0Long Xin Xiao1He Peng Fei2School of Mathematics, Northwest University, Xi'an, 710127, ChinaSchool of Mathematics, Northwest University, Xi'an, 710127, ChinaSchool of Mathematics and Information Science, Shaanxi Normal University, Xi'an, 710119, ChinaIn this paper, we use filters of an EQ-algebra E to induce a uniform structure (E, 𝓚), and then the part 𝓚 induce a uniform topology 𝒯 in E. We prove that the pair (E, 𝒯) is a topological EQ-algebra, and some properties of (E, 𝒯) are investigated. In particular, we show that (E, 𝒯) is a first-countable, zero-dimensional, disconnected and completely regular space. Finally, by using convergence of nets, the convergence of topological EQ-algebras is obtained.http://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0032/math-2017-0032.xml?format=INTuniform spacetopological eq-algebrafilterconverge sequence06f9954e15 |
| spellingShingle | Yang Jiang Long Xin Xiao He Peng Fei Uniform topology on EQ-algebras Open Mathematics uniform space topological eq-algebra filter converge sequence 06f99 54e15 |
| title | Uniform topology on EQ-algebras |
| title_full | Uniform topology on EQ-algebras |
| title_fullStr | Uniform topology on EQ-algebras |
| title_full_unstemmed | Uniform topology on EQ-algebras |
| title_short | Uniform topology on EQ-algebras |
| title_sort | uniform topology on eq algebras |
| topic | uniform space topological eq-algebra filter converge sequence 06f99 54e15 |
| url | http://www.degruyter.com/view/j/math.2017.15.issue-1/math-2017-0032/math-2017-0032.xml?format=INT |
| work_keys_str_mv | AT yangjiang uniformtopologyoneqalgebras AT longxinxiao uniformtopologyoneqalgebras AT hepengfei uniformtopologyoneqalgebras |