Generalized Metric Spaces Do Not Have the Compatible Topology
We study generalized metric spaces, which were introduced by Branciari (2000). In particular, generalized metric spaces do not necessarily have the compatible topology. Also we prove a generalization of the Banach contraction principle in complete generalized metric spaces.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/458098 |
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Article |
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doaj-ca8faa460b2d43ce8b65e7fcff6810282020-11-24T22:36:11ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/458098458098Generalized Metric Spaces Do Not Have the Compatible TopologyTomonari Suzuki0Department of Basic Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, JapanWe study generalized metric spaces, which were introduced by Branciari (2000). In particular, generalized metric spaces do not necessarily have the compatible topology. Also we prove a generalization of the Banach contraction principle in complete generalized metric spaces.http://dx.doi.org/10.1155/2014/458098 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Tomonari Suzuki |
| spellingShingle |
Tomonari Suzuki Generalized Metric Spaces Do Not Have the Compatible Topology Abstract and Applied Analysis |
| author_facet |
Tomonari Suzuki |
| author_sort |
Tomonari Suzuki |
| title |
Generalized Metric Spaces Do Not Have the Compatible Topology |
| title_short |
Generalized Metric Spaces Do Not Have the Compatible Topology |
| title_full |
Generalized Metric Spaces Do Not Have the Compatible Topology |
| title_fullStr |
Generalized Metric Spaces Do Not Have the Compatible Topology |
| title_full_unstemmed |
Generalized Metric Spaces Do Not Have the Compatible Topology |
| title_sort |
generalized metric spaces do not have the compatible topology |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2014-01-01 |
| description |
We study generalized metric spaces,
which were introduced by Branciari
(2000).
In particular,
generalized metric spaces do not necessarily have the compatible topology.
Also we prove a generalization of the Banach contraction principle
in complete generalized metric spaces. |
| url |
http://dx.doi.org/10.1155/2014/458098 |
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AT tomonarisuzuki generalizedmetricspacesdonothavethecompatibletopology |
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1725720846690942976 |