Force recurrence near zero
Manoranjan Singha, Ujjal Kumar Hom
TL;DR
This paper explores various types of recurrence and set properties near zero in dense subsemigroups of positive reals, establishing relations among them under countability assumptions.
Contribution
It introduces new concepts of recurrence and set properties near zero and analyzes their interrelations in dense subsemigroups of positive reals.
Findings
Characterization of recurrent points near zero
Relations among different recurrence set concepts
Impact of countability on set properties near zero
Abstract
Considering any dense subsemigroup of the additive semigroup of positive real numbers and a filter associated with it as the domain of thought, various concepts of sets like sets that forces recurrence near zero, sets that contains broken IP-set near near zero, sets that forces uniform recurrence near zero and sets that contains broken syndetic set near zero have been introduced and some relation among them are established by assuming countability of the said dense subsemigroup. The article begin with a characterization of recurrent point near zero.
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Taxonomy
TopicsNumerical Methods and Algorithms · Mathematical Dynamics and Fractals · Computability, Logic, AI Algorithms