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user74022
user74022
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Given a subset $S$ of a finite metric space $F$ with a distance function $d(,)$ and a number $\delta$$\delta > 0$ let $N_\delta(S) = \{x \in F| d(x,S)\ge \delta\}$. Is there a characterization of conditions necessary and sufficient for $N_\delta(N_\delta(S)) = S$ to hold?

Given a subset $S$ of a finite metric space $F$ with a distance function $d(,)$ and a number $\delta$ let $N_\delta(S) = \{x \in F| d(x,S)\ge \delta\}$. Is there a characterization of conditions necessary and sufficient for $N_\delta(N_\delta(S)) = S$ to hold?

Given a subset $S$ of a finite metric space $F$ with a distance function $d(,)$ and a number $\delta > 0$ let $N_\delta(S) = \{x \in F| d(x,S)\ge \delta\}$. Is there a characterization of conditions necessary and sufficient for $N_\delta(N_\delta(S)) = S$ to hold?

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user74022
user74022
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Conditions for a set being closed under taking complement of a ball twice

Given a subset $S$ of a finite metric space $F$ with a distance function $d(,)$ and a number $\delta$ let $N_\delta(S) = \{x \in F| d(x,S)\ge \delta\}$. Is there a characterization of conditions necessary and sufficient for $N_\delta(N_\delta(S)) = S$ to hold?