Interplay between strongly universal spaces and pairs
Volume 386 / 2000
Dissertationes Mathematicae 386 (2000), 1-38
MSC: 57N20
DOI: 10.4064/dm386-0-1
Abstract
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 $\mit\Omega$ we also study the question of topological uniqueness of the pair $(M,X)$, where $M=[0,1]^\omega$ or $M=(0,1)^\omega$ and $X$ is a copy of $\mit\Omega$ in $M$ having a locally homotopy negligible complement in~$M$.
