Let (X,d) be a metric space, and x is an element in X. Show that [tex]\{y \in X|d(y,x)>r\}[/tex] is open for all r in Reals.(adsbygoogle = window.adsbygoogle || []).push({});

I really need some help with this one, I have almost no idea on how I am meant to solve this.

The only thing i know is that I have to use the Openness definition, that states something like [tex]\forall x_0 \in U \exists r>0| B_r \in U[/tex], where in U is a subelement of the metric space (X,d).

But i don't know how to get started.

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# Homework Help: Metric Space, Show that it's open

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