On Statistical Boundedness of Metric Valued Sequences

Mehmet Küçükaslan, Uğur Değer

Abstract

In this work, statistical boundedness  is defined in a metric space
and, statistical boundedness of metric valued sequences and their
subsequences are studied. The interplay between the statistical
boundedness and boundedness in a metric spaces are also studied, and
it is shown that boundedness imply statistical boundedness and if
the number of elements of the metric space is finite then these two
concepts coincide. Moreover, here is given analogy of
Balzano-Weierstrass Theorem.

Keywords

Statistical convergence, metric spaces, statistical boundedness, asymptotic density

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