| Some Characterizations of Spaces with Weak Form of $cs$-Networks |
| Received:April 22, 2015 Revised:October 12, 2015 |
| Key Words:
sequence covering sequentially quotient $sn$-network $cs$-network
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| Fund Project:Supported by the Council of Scientific & Industrial Research Fellowship in Sciences (CSIR, New Delhi) for Meritorious Students, India. |
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| Abstract: |
| 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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2016.03.013 |
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