Dimension of metric spaces

C. H. Dowker and W. Hurewicz

A chapter in The Mathematical Legacy of Eduard Čech, 1993, pp 178-183 from Springer

Abstract: Abstract It is to be shown that a metric space has dimension ≤ n if and only if there exists a sequence {{ai} of locally finite open coverings, each of order ≤ n, with mesh tending to zero as i→∞, such that (a) the closure of each member of ai+1 is contained in some member of ai+1 is contained in some member of ai.

Keywords: Normal Space; Large Integer; Algebraic Topology; Dimension Theory; Finite Collection (search for similar items in EconPapers)
Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-7524-0_15

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DOI: 10.1007/978-3-0348-7524-0_15

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