Limit Theorem for Inverse Sequencesof Metric Spaces in Extension

We prove a limit theorem for extension theory for metric spaces. This theorem can be put in the following way. Suppose that K is a simplicial complex, jKj is given the weak topology, and a metrizable space X is the limit of an inverse sequence of metrizable spaces X i having the property that X i jKj for each i 2 N. Then XjKj. This latter property means that for each closed subset A of X and map f : A ! jKj, there exists a map F : X ! jKj which is an extension of f.