Closed set (metric spaces)
Suppose [itex]f:\mathbb{R}\to \mathbb{R}[/itex] is a continuous function (standard metric).
Show that its graph [itex]\{ (x,f(x)) : x \in \mathbb{R} \}[/itex] is a closed subset of [itex]\mathbb{R}^2[/itex] (Euclidean metric). How to show this is closed? 
Re: Closed set (metric spaces)
what are your definitions of closed?
thinking geometrically, a continuous function will have a graph that is an unbroken curve in the 2D plane, how would you show this is closed in R^2 
Re: Closed set (metric spaces)
Quote:

Re: Closed set (metric spaces)
How could I show it is closed by considering the function [itex]f : \mathbb{R}^2 \to \mathbb{R}[/itex] defined by [itex]f(x,y)=f(x) y[/itex]?

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