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...

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Bibliographic Details
Main Authors:	Sejal Shah, Ruchi Das, Tarun Das
Format:	Article
Language:	English
Published:	Universitat Politècnica de València 2016-10-01
Series:	Applied General Topology
Subjects:	topological specification property uniform entropy uniform spaces.
Online Access:	http://polipapers.upv.es/index.php/AGT/article/view/4555

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spelling	doaj-77ecdb32c39c4f11b987da3c0a60cf6f2020-11-25T00:05:05ZengUniversitat 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.
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Sejal Shah Ruchi Das Tarun Das
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.
author_facet	Sejal Shah Ruchi Das Tarun Das
author_sort	Sejal Shah
title	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_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_sort	note on uniform entropy for maps having topological specification property
publisher	Universitat Politècnica de València
series	Applied General Topology
issn	1576-9402 1989-4147
publishDate	2016-10-01
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.
topic	topological specification property uniform entropy uniform spaces.
url	http://polipapers.upv.es/index.php/AGT/article/view/4555
work_keys_str_mv	AT sejalshah anoteonuniformentropyformapshavingtopologicalspecificationproperty AT ruchidas anoteonuniformentropyformapshavingtopologicalspecificationproperty AT tarundas anoteonuniformentropyformapshavingtopologicalspecificationproperty AT sejalshah noteonuniformentropyformapshavingtopologicalspecificationproperty AT ruchidas noteonuniformentropyformapshavingtopologicalspecificationproperty AT tarundas noteonuniformentropyformapshavingtopologicalspecificationproperty
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A note on uniform entropy for maps having topological specification property

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