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BENEDICTtance less than 8ep from the point P, then X and P lie together in a connected sub-set of M every point of which is at a distance of less than e from the point P. The set M is said to be uniformly connected im kleinen if for every positive number e there exists a positive num- ber 68 such that if P1 and P2 are two points of M at a distance apart less than 58 then they lie together in a connected sub-set of M every point of which is at a distance of less than e from P1. Cf.
Harris et al. (Sun,) studied this question.