On Statistically Sequentially Covering Maps

Abstract

A mapping $f: X \rightarrow Y $ is statistically sequence covering map if whenever a sequence $\lbrace y_n \rbrace$  convergent to $y$ in $Y,$ there is a  sequence $\lbrace x_n \rbrace$ statistically converges to $x$ in $X$ with each $x_n \in f^{-1}(y_n) $ and $ x \in f^{-1}(y).$ In this paper, we introduce the concept of statistically sequence covering map which is a generalization of sequence covering map and discuss the relation with covering maps by some examples. Using this concept, we prove that every closed and statistically sequence-covering image of a metric space is metrizable. Also, we give characterizations of statistically sequence covering compact images of spaces with a weaker metric topology.