The topology of statistical convergence

Khdiga K Tabib, University of Texas at El Paso

Abstract

A sequence {xn} is said to be statistically convergent to ℓ provided that "almost all" of the values of { xn} are arbitrarily close to ℓ. One can also define what is meant by statistical limit point, statistical limit superior, statistical limit inferior of a sequence and so forth and thus create a theory of convergence that includes ordinary convergence. In this work we investigate all these concepts and prove some new results. We also introduce a topology defined by this new convergence which we call statistical topology. Then we prove that both the statistical topology and the regular topology are identical.

Subject Area

Mathematics

Recommended Citation

Tabib, Khdiga K, "The topology of statistical convergence" (2012). ETD Collection for University of Texas, El Paso. AAI1518242.
https://digitalcommons.utep.edu/dissertations/AAI1518242

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