Functional product topology: A common framework of the topological sum, the product topology and the functional topology of pointwise convergence
Based on the topological sum, for X being a discrete topological space, we prove that the product topology generated by some topological spaces is equal to the topology of pointwise convergence related to X. For every topology on a Cartesian product, we find an equivalent condition under which every...
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| Format: | Article |
| Language: | zho |
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Hebei University of Science and Technology
2015-08-01
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| Series: | Journal of Hebei University of Science and Technology |
| Subjects: | |
| Online Access: | http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201504008&flag=1&journal_ |
| _version_ | 1819212315505983488 |
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| author | Chong SHEN Wei YAO |
| author_facet | Chong SHEN Wei YAO |
| author_sort | Chong SHEN |
| collection | DOAJ |
| description | Based on the topological sum, for X being a discrete topological space, we prove that the product topology generated by some topological spaces is equal to the topology of pointwise convergence related to X. For every topology on a Cartesian product, we find an equivalent condition under which every projection from the product to each component is continuous. We propose the definition of functional product spaces, which can be considered as a common framework of the product spaces, the topological sums and the functional spaces (the topology of pointwise convergence). |
| first_indexed | 2024-12-23T06:41:01Z |
| format | Article |
| id | doaj.art-7f58617b274e41a089b32a8353849cca |
| institution | Directory Open Access Journal |
| issn | 1008-1542 |
| language | zho |
| last_indexed | 2024-12-23T06:41:01Z |
| publishDate | 2015-08-01 |
| publisher | Hebei University of Science and Technology |
| record_format | Article |
| series | Journal of Hebei University of Science and Technology |
| spelling | doaj.art-7f58617b274e41a089b32a8353849cca2022-12-21T17:56:42ZzhoHebei University of Science and TechnologyJournal of Hebei University of Science and Technology1008-15422015-08-0136439039310.7535/hbkd.2015yx04008b201504008Functional product topology: A common framework of the topological sum, the product topology and the functional topology of pointwise convergenceChong SHEN0Wei YAO1School of Science, Hebei University of Science and Tecnology, Shijiazhuang, Hebei 050018, ChinaSchool of Science, Hebei University of Science and Tecnology, Shijiazhuang, Hebei 050018, ChinaBased on the topological sum, for X being a discrete topological space, we prove that the product topology generated by some topological spaces is equal to the topology of pointwise convergence related to X. For every topology on a Cartesian product, we find an equivalent condition under which every projection from the product to each component is continuous. We propose the definition of functional product spaces, which can be considered as a common framework of the product spaces, the topological sums and the functional spaces (the topology of pointwise convergence).http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201504008&flag=1&journal_point-set topologyproduct topologytopological sumtopology of pointwise convergencefunctional product space |
| spellingShingle | Chong SHEN Wei YAO Functional product topology: A common framework of the topological sum, the product topology and the functional topology of pointwise convergence Journal of Hebei University of Science and Technology point-set topology product topology topological sum topology of pointwise convergence functional product space |
| title | Functional product topology: A common framework of the topological sum, the product topology and the functional topology of pointwise convergence |
| title_full | Functional product topology: A common framework of the topological sum, the product topology and the functional topology of pointwise convergence |
| title_fullStr | Functional product topology: A common framework of the topological sum, the product topology and the functional topology of pointwise convergence |
| title_full_unstemmed | Functional product topology: A common framework of the topological sum, the product topology and the functional topology of pointwise convergence |
| title_short | Functional product topology: A common framework of the topological sum, the product topology and the functional topology of pointwise convergence |
| title_sort | functional product topology a common framework of the topological sum the product topology and the functional topology of pointwise convergence |
| topic | point-set topology product topology topological sum topology of pointwise convergence functional product space |
| url | http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201504008&flag=1&journal_ |
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