A note on uniform entropy for maps having topological specification property

Sejal Shah; Ruchi Das; Tarun Das

doi:10.4995/agt.2016.4555

Authors

Sejal Shah The Maharaja Sayajirao University of Baroda
Ruchi Das University of Delhi
Tarun Das University of Delhi

DOI:

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

Keywords:

topological specification property, uniform entropy, uniform spaces

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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Author Biographies

Sejal Shah, The Maharaja Sayajirao University of Baroda

Assistant Professor.

Department of Mathematics.
Faculty of Science.

Ruchi Das, University of Delhi

Professor.

Department of Mathematics.

Faculty of Mathematical Sciences.

Tarun Das, University of Delhi

Professor.

Department of Mathematics.

Faculty of Mathematical Sciences.

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