Kolmogorovs extension theorem provides a natural mapping from the space of coherent hierarchies of an agents rst-order, second- order, etc. beliefs to the space of probability measures over the ex- ogenous parameters and the other agentsbelief hierarchies. Mertens and Zamir (1985) showed that, if the spaces of belief hierarchies are endowed with the product topology, then this mapping is a homeomor- phism. This paper shows that this mapping is also a homeomorphism if the spaces of belief hierarchies are endowed with the uniform weak topology of Chen et al. (2010) or the universal strategic topology of Dekel et al. (2006), both of which ensure that strategic behaviour exhibits desirable continuity properties.