Hausdorff continua and the uniform property of Effros

We continue our investigation of Hausdorff continua with the uniform property of Effros. We introduce the notion of a uniformly completely regular map to improve the uniform version of F. Burton Jones' Aposyndetic Decomposition Theorem given in On Jones' set function T and the property of Kelley for Hausdorff continua. We also extend Janusz R. Prajs' Mutual Aposyndetic Decomposition Theorem to Hausdorff continua with the uniform property of Effros. We show that the continuity of the set function T implies the continuity of the set function K, answering a question of David P. Bellamy.