## Tsukuba Journal of Mathematics

### Scalence metric spaces

Hisao Kato

#### 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