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Answer by Ailbe for Metric Spaces: Disjoint Open Sets
I'll assume that you know that open balls in a metric space are open sets. Then since $x_1$ and $x_2$ are distinct$$r = \frac{1}{2} d(x_1,x_2) > 0.$$Then the balls $B_{r}(x_1)$ and $B_{r}(x_2)$ are...
View ArticleMetric Spaces: Disjoint Open Sets
The following question is from Fred H. Croom's book "Principles of Topology"Let $(X,d)$ be a metric space and $x_1,x_2$ distinct points of $X$. Prove that there are disjoint open sets $O_1$ and $O_2$...
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