Sunday, 11 August 2013

What is $d(x,F_k)$, where $F_k\subset \Bbb{R}$?

What is $d(x,F_k)$, where $F_k\subset \Bbb{R}$?

Let $F_k\subset \Bbb{R}$ be an open interval in $\Bbb{R}$, and $x\in
\Bbb{R}$ a point. How is $d(x,F_k)$ defined? I came across this notation
in my textbook and it is confusing me. Is $d(x,F_k)=\min\{d(x,y)\},\forall
y\in F_k$? And if this definition is the correct one, then is it valid
only for bounded intervals $F_k\subset \Bbb{R}$?
Thank you!

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