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 On the duality of the space $X$ and the algebra $C_p(X)$ Bull. Korean Math. Soc. 1999 Vol. 36, No. 4, 717-722 sung Ki Park Chosun University Abstract : The set of continuous maps of a space $X$ to real usual space $R$ equipped with the topology of pointwise convergence will be denoted by $C_p (X)$. In this paper, we prove that: $C_p(X)$ is hereditarily separable and hereditary Lindel\"of if and only if $X^n$ is hereditarily separable and hereditary Lindelof. Keywords : density character, the topology of pointwise convergence, hereditarily separable, hereditary Lindelof MSC numbers : 54C35 Full-Text :