A note on uniform entropy for maps having topological specification property
We prove that if a uniformly continuous self-map $f$ of a uniform space has topological specification property then the map $f$ has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having specification property. An example is also provided...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Universitat Politècnica de València
2016-10-01
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| Series: | Applied General Topology |
| Subjects: | |
| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/4555 |
| _version_ | 1828300307614924800 |
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| author | Sejal Shah Ruchi Das Tarun Das |
| author_facet | Sejal Shah Ruchi Das Tarun Das |
| author_sort | Sejal Shah |
| collection | DOAJ |
| description | We prove that if a uniformly continuous self-map $f$ of a uniform space has topological specification property then the map $f$ has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having specification property. An example is also provided to justify that the converse is not true. |
| first_indexed | 2024-04-13T13:07:28Z |
| format | Article |
| id | doaj.art-77ecdb32c39c4f11b987da3c0a60cf6f |
| institution | Directory Open Access Journal |
| issn | 1576-9402 1989-4147 |
| language | English |
| last_indexed | 2024-04-13T13:07:28Z |
| publishDate | 2016-10-01 |
| publisher | Universitat Politècnica de València |
| record_format | Article |
| series | Applied General Topology |
| spelling | doaj.art-77ecdb32c39c4f11b987da3c0a60cf6f2022-12-22T02:45:43ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472016-10-0117212312710.4995/agt.2016.45554834A note on uniform entropy for maps having topological specification propertySejal Shah0Ruchi Das1Tarun Das2The Maharaja Sayajirao University of BarodaUniversity of DelhiUniversity of Delhi, DelhiWe prove that if a uniformly continuous self-map $f$ of a uniform space has topological specification property then the map $f$ has positive uniform entropy, which extends the similar known result for homeomorphisms on compact metric spaces having specification property. An example is also provided to justify that the converse is not true.http://polipapers.upv.es/index.php/AGT/article/view/4555topological specification propertyuniform entropyuniform spaces. |
| spellingShingle | Sejal Shah Ruchi Das Tarun Das A note on uniform entropy for maps having topological specification property Applied General Topology topological specification property uniform entropy uniform spaces. |
| title | A note on uniform entropy for maps having topological specification property |
| title_full | A note on uniform entropy for maps having topological specification property |
| title_fullStr | A note on uniform entropy for maps having topological specification property |
| title_full_unstemmed | A note on uniform entropy for maps having topological specification property |
| title_short | A note on uniform entropy for maps having topological specification property |
| title_sort | note on uniform entropy for maps having topological specification property |
| topic | topological specification property uniform entropy uniform spaces. |
| url | http://polipapers.upv.es/index.php/AGT/article/view/4555 |
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