Embedding metric spaces in Euclidean space |
| |
Authors: | C. L. Morgan |
| |
Affiliation: | (1) Department of Mathematics, California State University, 94542 Hayward, California, USA |
| |
Abstract: | In this paper, we give necessary and sufficient conditions for embedding a given metric space in Euclidean space. We shall introduce the notions of flatness and dimension for metric spaces and prove that a metric space can be embedded in Euclidean n-space if and only if the metric space is flat and of dimension less than or equal to n. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|