대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제61권1호
  • /
  • Pages.247-262
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  • 2024
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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TOPOLOGICAL SENSITIVITY AND ITS STRONGER FORMS ON SEMIFLOWS

  • Ruchi Das (Department of Mathematics University of Delhi) ;
  • Devender Kumar (Department of Mathematics University of Delhi) ;
  • Mohammad Salman (Department of Mathematics University of Delhi)
  • 투고 : 2023.02.17
  • 심사 : 2023.06.09
  • 발행 : 2024.01.31
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초록

In this paper we introduce and study the notions of topological sensitivity and its stronger forms on semiflows and on product semiflows. We give a relationship between multi-topological sensitivity and thick topological sensitivity on semiflows. We prove that for a Urysohn space X, a syndetically transitive semiflow (T, X, 𝜋) having a point of proper compact orbit is syndetic topologically sensitive. Moreover, it is proved that for a T3 space X, a transitive, nonminimal semiflow (T, X, 𝜋) having a dense set of almost periodic points is syndetic topologically sensitive. Also, wherever necessary examples/counterexamples are given.

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과제정보

The second author is supported by CSIR-SRF Sr. No. 09/045(1799)/2020-EMR-I for carrying out this research work.

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