V. RENUKADEVI,B. PRAKASH.Some Characterizations of Spaces with Weak Form of $cs$-Networks[J].数学研究及应用,2016,36(3):369~378
Some Characterizations of Spaces with Weak Form of $cs$-Networks
Some Characterizations of Spaces with Weak Form of $cs$-Networks

DOI：10.3770/j.issn:2095-2651.2016.03.013

 作者 单位 V. RENUKADEVI Department of Mathematics, ANJA College (Autonomous), Sivakasi 626 124, Tamil Nadu, India B. PRAKASH Department of Mathematics, ANJA College (Autonomous), Sivakasi 626 124, Tamil Nadu, India

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.

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.