By J. L. Dupont, I. H. Madsen

Collage of Aarhus, 50. Anniversary, eleven September 1978

**Read Online or Download Algebraic Topology, Aarhus 1978: Proceedings of a Symposium held at Aarhus, Denmark, August 7-12, 1978 PDF**

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**Extra info for Algebraic Topology, Aarhus 1978: Proceedings of a Symposium held at Aarhus, Denmark, August 7-12, 1978**

**Example text**

J f g A . gEF o In particular, for fE F

1i : 6 c o n t r a c t i o n s Fig. eI ,I L s u o [ . ,. Z ~' "~" '%~" ~ " . . 'P2 Lg 52 Fig. 19 : 3 c o n t r a c t i o n s Fig. 20 : 4 c o n t r a c t i o n s Fig. 21 : 4 contractions Fig. 22 : 4 Contractions Fig. 23 : 4 c o n t r a c t i o n s Fig. 5 of Chapter 2. However, by breaking down the contraction cA of J~X into the contractions ca of X where a E A, the map above is actually the contraction induced by F U {c a ] a E A} E Admis X . This is given in the next proposition along with a description of the invariant set.

Pro of: (1) 'C' is trivial. Now further suppose (An) is decreasing. Then for z E lim d (An) , z E s t A m for infinite m', and hence for all finite n we have (as A me_An *) z E s t ( A n * ) = "~n . 38 (2) 'C' is trivial. And if (An) is increasing we easily see that [J A n C lim d (An) , n hence (as the latter is dosed) [J A n c lim d (An). o n And in p a r t i c u l a r . . 4 Proposition For a sequence (An) in~dX, (I) If (An) is decreasing, (An) -~ ~ A n . (2) If (An) is increasing and bounded above in,~gX, (An) -~ ~n A n .

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