The Topology Of Statistical Convergence
Khdiga Kalifa Tabib · DigitalCommons@UTEP (The University of Texas at El Paso) · 2012
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.