# Strong convergence in topological spaces

### Abstract

Study of summability theory in an arbitrary topological space is not always an easy issue as many of the convergence methods need linear structure in the space. The concept of statistical convergence is one of the exceptional concepts of summability theory that can be considered in a topological space. There is a strong relationship between this convergence method and strong convergence which is another interesting concept of summability theory. However, dependence of the strong convergence to the metric, studying similar relationship directly in arbitrary Hausdorff spaces is not possible. In this paper we introduce a convergence method which extends the notion of strong convergence to topological spaces. This new definition not only helps us to investigate a similar relationship in a topological space but also leads to study a new type of convergence in topological spaces. We also give a characterization of statistical convergence.

**Key words:** Strong convergence, statistical convergence, Hausdorff space.