This article is an an acknowledgement for Maurice Fréchet for his remarks concerning the article entitled "Concerning the relation between separability and the proposition that every uncountable point set has a limit point" published in Fundamenta Mathematica VIII.
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The purpose of this article is to prove: Theorem: Suppose that, in a given three dimensional space S, ABCD is a rectangle and G is a self-compact set of simple continuous arcs such that: 1. through each point of ABCD there is just one arc of G, 2. BC and AD are arcs of G, 3. no two arcs of G have a point in common, 4. each arc of G has one endpoint on the interval AB and one endpoint on the interval CD but contains no other point in common with either of these intervals, 5. the set of arcs G is equicontinous. Then the point - set R composed of all the arcs of the set G is in one to one continuous correspondence with the plane point-set formed by a rectangle together with its interior.
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