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 or and X is a copy of Ω in M having a locally homotopy negligible complement in M.
@book{bwmeta1.element.bwnjournal-rm-doi-10_4064-dm386-0-1,
author = {Taras Banakh and Robert Cauty},
title = {Interplay between strongly universal spaces and pairs},
series = {GDML\_Books},
year = {2000},
zbl = {0954.57007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm386-0-1}
}
Taras Banakh; Robert Cauty. Interplay between strongly universal spaces and pairs. GDML_Books (2000), http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-rm-doi-10_4064-dm386-0-1/