## 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

### Keywords:

groups; preseminorms; invariant semimetrics; Galois connections
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### References:

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