✦ LIBER ✦

Light maps and extensional dimension

✍ Scribed by A.N. Dranishnikov; V.V. Uspenskij

Book ID: 104295175
Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 640 KB
Volume: 80
Category: Article
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(96)00164-2

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✦ Synopsis

We show that any light map f : X + Y between compact spaces admits a decomposition f = gh, where g : 2 + Y is a finite-to-one map of a special type and h : X + 2 has arbitrarily small fibers. It follows that light maps between compact spaces do not lower extensional dimension. Our theorem yields a positive answer to Problem 423 from "Open Problems in Topology". We also generalize Hurewicz' theorem on dimension-raising maps to the case of extensional dimension.

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