Can finite metric spaces be embedded into n-dimensional surfaces?

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Discussion Overview

The discussion focuses on the embedding of finite metric spaces into n-dimensional surfaces within R^n, exploring sufficient and necessary conditions related to the metric involved.

Discussion Character

  • Exploratory, Technical explanation

Main Points Raised

  • One participant seeks information on the conditions for embedding finite metric spaces into n-dimensional surfaces.
  • Another participant references Whitney's embedding theorem as a potential source of information.
  • A subsequent reply questions the relevance of Whitney's theorem specifically to metric spaces.
  • Another participant suggests looking into the Nash embedding theorem as an additional resource.

Areas of Agreement / Disagreement

The discussion does not reach a consensus, as participants express varying levels of understanding and relevance regarding the theorems mentioned.

Contextual Notes

Participants have not clarified the specific conditions or definitions related to the metrics in question, leaving some assumptions unaddressed.

Dragonfall
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I need to know about the embedding of finite metric spaces into n-dimensional surfaces in R^n. (sufficient/necessary conditions on the metric, etc). Can anyone point me towards a source?
 
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Yes but how does this relate to metric spaces?
 
Anyone?
 
Check out Nash embedding theorem, too.
 

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