In a paper on continuous curves printed in the BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, July, 1923, you have raised the question, whether an arc lying in a threedimensional space is accessible at each of its ends from every point which does not lie on it. I shall answer positively this question. Let AB be an arc lying in the space S, X a point of S-AB, P a point of AB (not necessarily an end-point). Let Sbe a plane containing the points X and P. The point-set G, composed of those points

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... the arc AB which lie on H, is a closed plane and bounded set. Since the arc AB passes through G, the set G does obviously satisfy a condition (which you gave with Professor Kline in a paper printed in ANNALS OF MATHEMATICS)* which is necessary and sufficient in order that it should be possible to pass an arc through it. Let T be an arc lying on H, containing G but not X Hence T is accessible at each of its points on the plane H (see, e. g., Schoenflies). Let XP be an arc lying on H and having in common with T only the point P. Hence XP has in common with AB only the point P and thus the theorem is proved. Obviously the proof holds true in n-dimensional space, THE UNIVERSITY OF WARSAW * The paper here referred to is On the most general plane closed point-set through which it is possible to pass a simple continuous arc.