# The topology of statistical convergence

#### Abstract

A sequence {*x _{n}*} is said to be statistically convergent to ℓ provided that "almost all" of the values of {

*x*} 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. ^

_{n}#### 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