The topology of statistical convergence
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
Khdiga K Tabib,
"The topology of statistical convergence"
(January 1, 2012).
ETD Collection for University of Texas, El Paso.
Paper AAI1518242.
http://digitalcommons.utep.edu/dissertations/AAI1518242