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 3 replaced http://math.stackexchange.com/ with https://math.stackexchange.com/ edited Apr 13 '17 at 12:22 Reopened This Question Two disjoint closed sets $$A,B \subset \mathbb{R}$$ such that there does not exist (positive) $$\varepsilon$$ with $$d(A,B) \gt \varepsilon$$Two disjoint closed sets $$A,B \subset \mathbb{R}$$ such that there does not exist (positive) $$\varepsilon$$ with $$d(A,B) \gt \varepsilon$$ was mistakenly marked as a duplicate due to my overlooking the requirement that $$A,B$$ are subsets of $$\mathbb{R}$$. The faux duplicate concerns two closed subsets of the plane. Little help? Reopened This Question Two disjoint closed sets $$A,B \subset \mathbb{R}$$ such that there does not exist (positive) $$\varepsilon$$ with $$d(A,B) \gt \varepsilon$$ was mistakenly marked as a duplicate due to my overlooking the requirement that $$A,B$$ are subsets of $$\mathbb{R}$$. The faux duplicate concerns two closed subsets of the plane. Little help? Reopened This Question Two disjoint closed sets $$A,B \subset \mathbb{R}$$ such that there does not exist (positive) $$\varepsilon$$ with $$d(A,B) \gt \varepsilon$$ was mistakenly marked as a duplicate due to my overlooking the requirement that $$A,B$$ are subsets of $$\mathbb{R}$$. The faux duplicate concerns two closed subsets of the plane. Little help? 2 question reopened edited Feb 4 '16 at 23:19 hardmath 29.9k22 gold badges4141 silver badges8080 bronze badges Reopened This Question Two disjoint closed sets $$A,B \subset \mathbb{R}$$ such that there does not exist (positive) $$\varepsilon$$ with $$d(A,B) \gt \varepsilon$$ was mistakenly marked as a duplicate due to my overlooking the requirement that $$A,B$$ are subsets of $$\mathbb{R}$$. The faux duplicate concerns two closed subsets of the plane. Little help? This Question Two disjoint closed sets $$A,B \subset \mathbb{R}$$ such that there does not exist (positive) $$\varepsilon$$ with $$d(A,B) \gt \varepsilon$$ was mistakenly marked as a duplicate due to my overlooking the requirement that $$A,B$$ are subsets of $$\mathbb{R}$$. The faux duplicate concerns two closed subsets of the plane. Little help? Reopened This Question Two disjoint closed sets $$A,B \subset \mathbb{R}$$ such that there does not exist (positive) $$\varepsilon$$ with $$d(A,B) \gt \varepsilon$$ was mistakenly marked as a duplicate due to my overlooking the requirement that $$A,B$$ are subsets of $$\mathbb{R}$$. The faux duplicate concerns two closed subsets of the plane. Little help? 1 answered Feb 4 '16 at 22:53 hardmath 29.9k22 gold badges4141 silver badges8080 bronze badges This Question Two disjoint closed sets $$A,B \subset \mathbb{R}$$ such that there does not exist (positive) $$\varepsilon$$ with $$d(A,B) \gt \varepsilon$$ was mistakenly marked as a duplicate due to my overlooking the requirement that $$A,B$$ are subsets of $$\mathbb{R}$$. The faux duplicate concerns two closed subsets of the plane. Little help?