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A natural Galois connection between generalized norms and metrics. (English) Zbl 06869859

Summary: 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 \(\mathbb{R}\) and \(X^2\) to \(\mathbb{R}\).

MSC:

06A15 Galois correspondences, closure operators (in relation to ordered sets)
20A99 Foundations
54E25 Semimetric spaces
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