Characterizing compact metrizable spaces among completely regular spaces

by    C. Richter, I. Stephani

Preprint series: 99-52, Reports on Analysis

Preprint series: , Reports on Analysis

54C30 Real-valued functions, See also {26-XX}
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54D30 Compactness
54E35 Metric spaces, metrizability

Abstract: Compact metrizable spaces are characterized
within the class of completely regular spaces by an external
property concerning the approximation of real-valued bounded
continuous functions by step functions. Moreover, an
internal characterization by a contraction property for
sequences of partitions of the space is presented.

Keywords: completely regular spaces, characterizing compact metrizable spaces, approximation of real-valued continuous functions by step functions, sequences of partitions

Upload: 1999-12-17

Update: 1999-12-17

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