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Perfect Maps and Relatively Discrete Collections
Author(s) -
BURKE DENNIS K.,
HANSELL ROGER W.
Publication year - 1996
Publication title -
annals of the new york academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.712
H-Index - 248
eISSN - 1749-6632
pISSN - 0077-8923
DOI - 10.1111/j.1749-6632.1996.tb36796.x
Subject(s) - corollary , discrete space , invariant (physics) , mathematics , cover (algebra) , pure mathematics , computer science , mathematical analysis , mechanical engineering , engineering , mathematical physics
We show that the image of a s̀‐relatively discrete cover of a space under a perfect map has a s̀‐relatively discrete refinement. From this we deduce that spaces with a s̀‐relatively discrete network and, in particular, s̀‐relatively discrete sets, are invariant under perfect maps. Another corollary is that weakly s̀‐refinable spaces are preserved by perfect maps, a result previously shown by the first author.