Force recurrence 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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