Some Characterizations of Spaces with Weak Form of $cs$-Networks

中文关键词:  sequence covering  sequentially quotient  $sn$-network  $cs$-network

英文关键词:sequence covering  sequentially quotient  $sn$-network  $cs$-network

中文摘要:

      In this paper, we introduce the concept of statistically sequentially quotient map: A mapping $f: X \rightarrow Y$ is statistically sequentially quotient map if whenever a convergent sequence $S$ in $Y,$ there is a convergent sequence $L$ in $X$ such that $f(L)$ is statistically dense in $S$. Also, we discuss the relation between statistically sequentially quotient map and covering maps by characterizing statistically sequentially quotient map and we prove that every closed and statistically sequentially quotient image of a $g$-metrizable space is $g$-metrizable. Moreover, we discuss about the preservation of generalization of metric space in terms of weakbases and $sn$-networks by closed and statistically sequentially quotient map.

英文摘要:

      In this paper, we introduce the concept of statistically sequentially quotient map: A mapping $f: X \rightarrow Y$ is statistically sequentially quotient map if whenever a convergent sequence $S$ in $Y,$ there is a convergent sequence $L$ in $X$ such that $f(L)$ is statistically dense in $S$. Also, we discuss the relation between statistically sequentially quotient map and covering maps by characterizing statistically sequentially quotient map and we prove that every closed and statistically sequentially quotient image of a $g$-metrizable space is $g$-metrizable. Moreover, we discuss about the preservation of generalization of metric space in terms of weakbases and $sn$-networks by closed and statistically sequentially quotient map.