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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.
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.
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.