On metrization of the space Dα[0, ∞)
A complete metric on the function space Dα[0, ∞) , which is a subspace of the space Dα[0, ∞) of functions without discontinuities of the second kind, is constructed. This metric converts Dα[0, ∞) into a complete separable metric space. It is a modification of a metric on Dα[0, 1) introduced by Wood...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2001-12-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/34423 |
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| _version_ | 1825197257925853184 |
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| author | Rimas Banys |
| author_facet | Rimas Banys |
| author_sort | Rimas Banys |
| collection | DOAJ |
| description |
A complete metric on the function space Dα[0, ∞) , which is a subspace of the space Dα[0, ∞) of functions without discontinuities of the second kind, is constructed. This metric converts Dα[0, ∞) into a complete separable metric space. It is a modification of a metric on Dα[0, 1) introduced by Woodroofe, and is stronger than the well-known metrics on Dα[0, ∞). Conditions for compactmess of the subsets of Dα[0, ∞) are given.
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| format | Article |
| id | doaj-art-90df04755536471a9605bc25b0583187 |
| institution | Kabale University |
| issn | 0132-2818 2335-898X |
| language | English |
| publishDate | 2001-12-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Lietuvos Matematikos Rinkinys |
| spelling | doaj-art-90df04755536471a9605bc25b05831872025-02-11T18:14:38ZengVilnius University PressLietuvos Matematikos Rinkinys0132-28182335-898X2001-12-0141spec.10.15388/LMR.2001.34423On metrization of the space Dα[0, ∞)Rimas Banys0Vilnius Gediminas Technical University A complete metric on the function space Dα[0, ∞) , which is a subspace of the space Dα[0, ∞) of functions without discontinuities of the second kind, is constructed. This metric converts Dα[0, ∞) into a complete separable metric space. It is a modification of a metric on Dα[0, 1) introduced by Woodroofe, and is stronger than the well-known metrics on Dα[0, ∞). Conditions for compactmess of the subsets of Dα[0, ∞) are given. https://www.zurnalai.vu.lt/LMR/article/view/34423 |
| spellingShingle | Rimas Banys On metrization of the space Dα[0, ∞) Lietuvos Matematikos Rinkinys |
| title | On metrization of the space Dα[0, ∞) |
| title_full | On metrization of the space Dα[0, ∞) |
| title_fullStr | On metrization of the space Dα[0, ∞) |
| title_full_unstemmed | On metrization of the space Dα[0, ∞) |
| title_short | On metrization of the space Dα[0, ∞) |
| title_sort | on metrization of the space dα 0 ∞ |
| url | https://www.zurnalai.vu.lt/LMR/article/view/34423 |
| work_keys_str_mv | AT rimasbanys onmetrizationofthespaceda0 |