# Open and closed sets in R^n

## Homework Statement

Let A be a subset of Rn and let $$\vec{w}$$ be a point in Rn. Show that A is open if and only if A + $$\vec{w}$$ is open.
Show that A is closed if and only if A + $$\vec{w}$$ is closed.

## Homework Equations

The translate of A by $$\vec{w}$$ is defined by
A + $$\vec{w}$$ := {$$\vec{w}$$ + $$\vec{u}$$ | $$\vec{u}$$ in A}

## The Attempt at a Solution

I tried to solve this componentwise:
$$\vec{u}$$ = {pi(ui)}, 1<=i<=n, so that $$\vec{u}$$ + $$\vec{w}$$ = {pi(ui) +pi(ui)}
But I'm not all that sure whether I'm on the right track..!

## Answers and Replies

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