On the Fuzzy Number Space with the Level Convergence Topology
We characterize compact sets of 𝔼1 endowed with the level convergence topology τℓ. We also describe the completion (𝔼1̂,𝒰̂) of 𝔼1 with respect to its natural uniformity, that is, the pointwise uniformity 𝒰, and show other topological properties of 𝔼1̂, as separability. We apply these results to give...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/326417 |
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| _version_ | 1832553430446505984 |
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| author | J. J. Font A. Miralles M. Sanchis |
| author_facet | J. J. Font A. Miralles M. Sanchis |
| author_sort | J. J. Font |
| collection | DOAJ |
| description | We characterize compact sets of 𝔼1 endowed with the level convergence topology τℓ. We also describe the completion (𝔼1̂,𝒰̂) of 𝔼1 with respect to its natural uniformity, that is, the pointwise uniformity 𝒰, and show other topological properties of 𝔼1̂, as separability. We apply these results to give an Arzela-Ascoli theorem for the space of (𝔼1,τℓ)-valued continuous functions on a locally compact topological space equipped with the compact-open topology. |
| format | Article |
| id | doaj-art-db5d6486914848b28daa89e87ad1c091 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-db5d6486914848b28daa89e87ad1c0912025-02-03T05:54:02ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/326417326417On the Fuzzy Number Space with the Level Convergence TopologyJ. J. Font0A. Miralles1M. Sanchis2Institut de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainInstitut de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainInstitut de Matemàtiques i Aplicacions de Castelló (IMAC), Universitat Jaume I, Campus del Riu Sec. s/n, 12071 Castelló, SpainWe characterize compact sets of 𝔼1 endowed with the level convergence topology τℓ. We also describe the completion (𝔼1̂,𝒰̂) of 𝔼1 with respect to its natural uniformity, that is, the pointwise uniformity 𝒰, and show other topological properties of 𝔼1̂, as separability. We apply these results to give an Arzela-Ascoli theorem for the space of (𝔼1,τℓ)-valued continuous functions on a locally compact topological space equipped with the compact-open topology.http://dx.doi.org/10.1155/2012/326417 |
| spellingShingle | J. J. Font A. Miralles M. Sanchis On the Fuzzy Number Space with the Level Convergence Topology Journal of Function Spaces and Applications |
| title | On the Fuzzy Number Space with the Level Convergence Topology |
| title_full | On the Fuzzy Number Space with the Level Convergence Topology |
| title_fullStr | On the Fuzzy Number Space with the Level Convergence Topology |
| title_full_unstemmed | On the Fuzzy Number Space with the Level Convergence Topology |
| title_short | On the Fuzzy Number Space with the Level Convergence Topology |
| title_sort | on the fuzzy number space with the level convergence topology |
| url | http://dx.doi.org/10.1155/2012/326417 |
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