(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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}

3. 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..!

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# Homework Help: Open and closed sets in R^n

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