On the Dimension of Perfectly Normal Spaces

Eduard Čech

A chapter in The Mathematical Legacy of Eduard Čech, 1993, pp 130-148 from Springer

Abstract: Abstract I modify slightly the recursive definition (Menger and Urysohn) of the dimension. In the case of separable spaces, up to now the only case studied, the modification is purely formal. I prove 1° the theorem on the dimension of a subset, 2° the theorem on the dimension of a sum (Summensatz), and 3° the theorem on the covering of a finite dimensional space (Zerlegungssatz) for very general spaces comprising as a particular case the metric spaces (metrische Räume).

Date: 1993
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-7524-0_11

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DOI: 10.1007/978-3-0348-7524-0_11

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