# Interior, Closure and Boundary of sets

• Nov 18th 2011, 08:41 AM
fylth
Interior, Closure and Boundary of sets
A little topology (I think) problem here:

For A:= [0,1) ∪ ([2,3] ∩ http://upload.wikimedia.org/wikipedi...d9cf5fa79f.png) ∪ {5} ⊂ R (real numbers) find the closure, boundary and interior of A

I know the definitions but I don't know how to actually calculate them
• Nov 18th 2011, 08:45 AM
girdav
Re: Interior, Closure and Boundary of sets
To compute the closure, just notice that the closure of a finite union is the union of the closures.
For the interior, can the points of $\displaystyle \left[2,3\right]\cap \mathbb Q$ be in it? And what about $\displaystyle \left\{5\right\}$?
• Nov 18th 2011, 08:52 AM
Plato
Re: Interior, Closure and Boundary of sets
Quote:

Originally Posted by fylth
For A:= [0,1) ∪ ([2,3] ∩ http://upload.wikimedia.org/wikipedi...d9cf5fa79f.png) ∪ {5} ⊂ R (real numbers) find the closure, boundary and interior of A

Do you know that $\displaystyle \overline{A\cup B}=\overline{A}\cup\overline{B}~?$

$\displaystyle \overline{[0,1)}=[0,1],~\overline{[2,3]\cap\mathbb{Q}}=[2,3],~\&~\overline{\{5\}}=\{5\}$
• Nov 18th 2011, 11:48 AM
TheChaz
Re: Interior, Closure and Boundary of sets
The boundary is the closure toss (set difference) the set...
The interior is...