On Statistically Sequentially Covering Maps


V. Renukadevi, B. Prakash




A mapping $f\colon X\to \Upsilon$ is statistically sequence covering map if whenever a sequence $\{y_n\}$ convergent to $y$ in $\Upsilon$, there is a sequence $\{x_n\}$ 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.