Local n-connectivity of decomposition spaces |
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| Authors: | J Dydak J Segal |
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| Institution: | Department of Mathematics, University of Washington, Seattle, WA 98195, USA |
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| Abstract: | A corollary of the main result of this paper is the following Theorem. Suppose f: X → Y is a closed surjection of metrizable spaces whose point inverses are LCn + 1-divisors (n ? 1). If Y is complete and f is homology n-stable, then Y is LCn + 1provided X is LCn + 1.Intuitively, f is homology n-stable if the ?ech homology groups of its point inverses are locally constant up to dimension n. In addition, we obtain sufficient conditions for the Freudenthal compactification to be LCn. |
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| Keywords: | Primary 54F35 54B15 Secondary 54D30 decompositions stability of pro-groups Mittag-Leffler condition |
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