A note on uniform entropy for maps having topological specification property

Sejal Shah

India

The Maharaja Sayajirao University of Baroda

Assistant Professor.

Department of Mathematics.
Faculty of Science.

Ruchi Das

India

University of Delhi

Professor.

Department of Mathematics.

Faculty of Mathematical Sciences.

Tarun Das

India

University of Delhi

Professor.

Department of Mathematics.

Faculty of Mathematical Sciences.

Submitted: 2016-01-18

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Accepted: 2016-07-12

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Published: 2016-10-03

DOI: https://doi.org/10.4995/agt.2016.4555
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Keywords:

topological specification property, uniform entropy, uniform spaces

Supporting agencies:

The second author is supported by UGC Major Research Project F.N. 42-25/2013(SR)

Abstract:

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.

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