In 1999, Arhangel'skii defined the following property: A Hausdorff topological space X is called k-Fréchect Urysohn if for every open subset A of X and every x in the closure of A there exists a sequence of points of A converging to x. We discuss the properties of k-Fréchect Urysohn spaces, the conditions under which a k-Fréchect Urysohn space is Fréchect Urysohn, and the behavior of k-Fréchect Urysohn spaces under products. Two questions are posed.
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