Physiology: Harris and Benedict

tance 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 setM is said to be uniformly connected im kleinen if for every positive number e there exists a positive number 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. Hahn, H., Jahresber. D. Math. Ver., Leipzig, 23, 1914, (318-322). 6 Hausdorff, F., Grundzilge der Mengenlehre, Veit & Co., Leipzig, 1914. 7 Cf. my paper, A theorem concerning continuous curves, Bull. Amer. Math. Soc., 23, 1917, (233-236). 8 Cf. Theorem 43 of my paper, On the foundations of plane analysis situs, Trans. Amer. Math. Soc., New York, 17, 1916, (131-164). I take this opportunity to correct an error in the statement of Theorem 44 of this paper. In this statement the upper 'interior' and the two upper 'without's are to be omitted.