Can a Wild Metric on a 2D Disc Prevent Isometric Embedding in R^3?

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Can you show me a metric on the 2 dimensional disc so wild that no open subset can be embedded in R^3?
 
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Embedded isometrically? Otherwise, it's false.
 
zhentil said:
Embedded isometrically? Otherwise, it's false.

yes. No open subset can be embedded isometrically in R^3
 

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