Hello,(adsbygoogle = window.adsbygoogle || []).push({});

I know how to start but I don't know how to end that proof. It's supposed to be easy:

Let S a subset of Rn.

PROVE THAT the boundary of S is a closed set.

(I'll use d for delta, so dS is my convention for "the boundary of S").

So here I go:

dS is closed iff it contains all of its boundary points,

so dS is closed iff d(dS) is included in dS.

Let x be any point such that x belongs to d(dS).

So for any Ball B(r, x), r>0, (ie centered at x),

| B intersection dS is not empty

| and B interesection (dS)complement is not empty.

(the second line is equivalent to) B interesection (interiorOfS union exteriorOfS) is not empty

Now what's next??

Thanks for your suggestions. If you do have a suggestion, please don't skip a step or don't bypass a detail because it seems obvious (trust me, nothing is obvious to the one who doesn't know yet!)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simple analysis question

**Physics Forums | Science Articles, Homework Help, Discussion**