Tsukuba Journal of Mathematics

Scalence metric spaces

Hisao Kato

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Abstract

In this paper, we introduce the notion of scalene metric and study it. In particular, we prove that a compactum with scalene metric is an AR and a locally compact space with locally scalene metric is an ANR. Also, we show that scalene metric subsets of a metric space play important roles as convex subsets of a Banach space in some selection theorems, and the notion of scalene metric gives another aspect which differs from that of E.Michael with respect to the constructions of selections ([6],[7],[8] and [9])

Article information

Source
Tsukuba J. Math., Volume 9, Number 1 (1985), 143-157.

Dates
First available in Project Euclid: 30 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.tkbjm/1496160198

Digital Object Identifier
doi:10.21099/tkbjm/1496160198

Mathematical Reviews number (MathSciNet)
MR794666

Citation

Kato, Hisao. Scalence metric spaces. Tsukuba J. Math. 9 (1985), no. 1, 143--157. doi:10.21099/tkbjm/1496160198. https://projecteuclid.org/euclid.tkbjm/1496160198


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