- #1

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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?

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- #1

- 446

- 0

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?

- #2

Homework Helper

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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

- #3

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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

Well a set [itex]A[/itex] is closed if [itex]\partial A \subset A[/itex], i.e. [itex]\partial A \cap A^c = \emptyset[/itex]

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