Some Characterizations of Spaces with Weak Form of $cs$-Networks |
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Authors: | V RENUKADEVI and B PRAKASH |
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Institution: | Department of Mathematics, ANJA College (Autonomous), Sivakasi 626 124, Tamil Nadu, India and Department of Mathematics, ANJA College (Autonomous), Sivakasi 626 124, Tamil Nadu, 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. |
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Keywords: | sequence covering sequentially quotient $sn$-network $cs$-network |
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