On invariant distributionally scrambled sets in non-compact systems

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Naveenkumar Yadav
Sejal Shah

Abstract

We study here the invariance of topological distributionally scrambled sets for maps on uniform spaces (not necessarily compact or metrizable). For a uniformly continuous surjective self-map defined on a uniformly locally compact Hausdorff uniform space having topological weak specification, a fixed point, and countably many periodic points with distinct periods, we prove that the map admits an invariant topological distributionally scrambled set of type 1. Further, if the uniform space is second countable, the map admits a dense Mycielski invariant topological distributionally scrambled set of type 1.

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How to Cite
Yadav, N., & Shah, S. (2025). On invariant distributionally scrambled sets in non-compact systems. Gulf Journal of Mathematics, 19(1), 40-48. https://doi.org/10.56947/gjom.v19i1.2442
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Author Biography

Naveenkumar Yadav, Department of Mathematics, B. K. M. Science College, India

Assistant Professor,

Department of Mathematics,

B. K. M. Science College,

Valsad-396001, Gujarat, India