CONVERGENCE TOPOLOGIES AND f-STATISTICALLY CAUCHY SEQUENCES

Abstract

Modulus statistical convergence has already been transported to the general scope of uniform spaces. Here, the novel notion of f∗-statistically Cauchy sequence is introduced and studied in uniform spaces. Certain properties are verified, in particular, the relationship between f∗-statistically Cauchy sequences and f-statistically Cauchy sequences is unveiled. Finally, f-statistical limit points and fstatistical cluster points of a sequence are considered and studied, again in the general context of uniform spaces.