Let W(·) denote a Wiener process. The functional law of the iterated logarithm due to Strassen (1964) establishes that the sequence {(2nLLn) ^-1/2 W(ns)} of functions of s∈[0,1] is almost surely compact in the uniform topology, and gives a simple description of the corresponding limit set. In this paper, we obtain a general characterization of the topologies under which this statement remains valid.