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1. In this paper we treat of continuous curvest in n-dimensional euclidean space; the arguments, excepting the use of inversion,t are established in more general space.? The principal theorems are devoted to the relation of such curves to the Janiszewski-Mullikin Theorem. This, stated generally, is to the effect that two bounded? subcontinua of a space, C, neither of which disconnects C, can disconnect C in their sum if and only if their product is not connected.** The theorem is shown to characterise, among bounded cyclicly connected t t continuous curves, the simple closed surface; t t among bounded continuous curves in general, those whose maximal cyclicly connected subsets are simple closed surfaces; among unbounded cyclicly connected continuous curves, the cylinder-trees;?? and, in general, unbounded

A study of continuous curves and their relation to the Janiszewski-Mullikin theorem