Technical Report No. 2014-4 : Continuous Selections of Modulus of Continuity (AU-Cas-Mathstats)

The main result of this thesis deals with continuous functions on metric spaces. Specifically, we show that given a continuous function f from a metric space (M1; d1) to a metric space (M2; d2), there is a function such that is continuous. The above result was established by Enayat in [Ena00] using the machinery of partitions of unity. Our expository account of Enayat’s paper contains a substantial body of results in general topology, including a thorough discussion of paracompact spaces and partitions of unity.