EN
Given a pair (M,X) of spaces we investigate the connections between the (strong) universality of (M,X) and that of the space X. We apply this to prove Enlarging, Deleting, and Strong Negligibility Theorems for strongly universal and absorbing spaces. Given an absorbing space Ω we also study the question of topological uniqueness of the pair (M,X), where $M = [0,1]^{ω}$ or $M = (0,1)^{ω}$ and X is a copy of Ω in M having a locally homotopy negligible complement in M.