In a recent paper,f G. T. Whyburn gave an example, in threedimensional space, of an arcwise connected and connected im kleinen point set which is not arcwise connected im kleinen, and raised the question as to whether such a set can exist in the plane; also, whether there exists in the plane a strongly connected and connected im kleinen set which is not strongly connected im kleinen. The purpose of this note is to answer both of these questions affirmatively. Indeed, there exists in the plane a

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... point set M which is arcwise connected and connected im kleinen, but which fails at every point to be strongly connected im kleinen. Let S denote the set of all points of the plane that lie within or on the square whose vertices are the points (0,0), (1,0), (1,1), (0,1); denote these vertices by A, B, C, D, respectively. The open interval is the sum of c (where c is the cardinal number of the continuum) mutually exclusive sets each of which is dense in AB.% Denote the class of these sets by X. Let K denote the class of all continua contained in 5, which contain at least one point of each of the straight line intervals AD and BC, but no point of AB or CD. This class has the cardinal number c. There exists a one-to-one correspondence, T, between the elements of the classes X and K. Let E(X) and E(K) be elements of X and K, respectively, which correspond to one another under T. Then, if x is a point of E(X), denote by l x the set of points of S that lie on the vertical line through x, and let P x denote the * Presented to the Society, December 31, 1930. f Concerning points of continuous curves defined by certain im kleinen properties,