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
投稿时间:2015-04-22  最后修改时间:2015-10-12
DOI:10.3770/j.issn:2095-2651.2016.03.013
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
基金项目:Supported by the Council of Scientific & Industrial Research Fellowship in Sciences (CSIR, New Delhi) for Meritorious Students, India.
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 
摘要点击次数: 813
全文下载次数: 960
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.
查看全文  查看/发表评论  下载PDF阅读器