- #1

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## Homework Statement

Let A be a subset of R

^{n}and let [tex]\vec{w}[/tex] be a point in R

^{n}. Show that A is open if and only if A + [tex]\vec{w}[/tex] is open.

Show that A is closed if and only if A + [tex]\vec{w}[/tex] is closed.

## Homework Equations

The translate of A by [tex]\vec{w}[/tex] is defined by

A + [tex]\vec{w}[/tex] := {[tex]\vec{w}[/tex] + [tex]\vec{u}[/tex] | [tex]\vec{u}[/tex] in A}

## The Attempt at a Solution

I tried to solve this componentwise:

[tex]\vec{u}[/tex] = {p

_{i}(u

_{i})}, 1<=i<=n, so that [tex]\vec{u}[/tex] + [tex]\vec{w}[/tex] = {p

_{i}(u

_{i}) +p

_{i}(u

_{i})}

But I'm not all that sure whether I'm on the right track..!