# Article

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Keywords:
distance functions and inequality relations; closure operators and Galois connections; Lipschitz and monotone functions; fixed points
Summary:
Following the ideas of R. DeMarr, we establish a Galois connection between distance functions on a set $S$ and inequality relations on $X_{S}=S \times \mathbb{R}$. Moreover, we also investigate a relationship between the functions of $S$ and $X_{S}$.
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