A natural Galois connection between generalized norms and metrics

Abstract

Having in mind a well-known connection between norms and metrics on vector spaces, for an additively written group X, we establish a natural Galois connection between functions of X to ℝ and X2 to ℝ.

Keywords

• groups
• preseminorms
• invariant semimetrics
• galois connections
• o6a15
• 20a99
• 54e25