Talk:Perfect map
Add topicLatest comment: 11 years ago by 89.77.121.156 in topic Untitled
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Untitled
[edit]Could someone please fix up some notation (such as writing p: X->Y properly and writing the inverse of p properly)
Thankyou Topology Expert (talk) 12:06, 13 June 2008 (UTC)
I do not believe that 10 or 11 are true as they read. Counterexamples:
10. If F is a closed subspace of X, then the inclusion if F in X is perfect, but it is not a quotient map.
11. Let G=Z act on X=R by translations. Then the projection from R to R/Z is not perfect. (For example, the kernel is not compact...) — Preceding unsigned comment added by 24.222.162.70 (talk) 02:14, 14 March 2012 (UTC)
Actually, I believe 10 and 11 are correct.
Ad 10. The definition requires map to be surjective Ad 11. Z is not a compact group. --89.77.121.156 (talk) 21:53, 22 August 2014 (UTC)