# Relationship of Boundaries

• Jul 12th 2011, 03:18 PM
aldrincabrera
Relationship of Boundaries
,.,just wondering..

what is the relationship of boundary(A intersection B) to boundary(A) and boundary(B)???
• Jul 12th 2011, 04:04 PM
Drexel28
Re: Relationship of Boundaries
Quote:

Originally Posted by aldrincabrera
,.,just wondering..

what is the relationship of boundary(A intersection B) to boundary(A) and boundary(B)???

What do you think, what does your intuition tell you? What about something like $\displaystyle (a,b),(b,c)$? What is $\displaystyle \partial((a,b)\cap (b,c))$? What about $\displaystyle \partial(a,b)\cap\partial(b,c)$?
• Jul 12th 2011, 10:30 PM
aldrincabrera
Re: Relationship of Boundaries
,.,.i have this silly intuition.,.,.my intuition says that boundary(A intersection B) is a subset of boundary(A) and boundary(B),.,i know im wrong,.,.hahahah
• Jul 12th 2011, 11:56 PM
FernandoRevilla
Re: Relationship of Boundaries
Quote:

Originally Posted by aldrincabrera
,.,.i have this silly intuition.,.,.my intuition says that boundary(A intersection B) is a subset of boundary(A) and boundary(B),.,i know im wrong,.,.hahahah

Yes, you are wrong :). In $\displaystyle \mathbb{R}$ with the usual topology choose $\displaystyle A=[0,2],\;B=[1,3]$ . Then, $\displaystyle \partial(A\cap B)=\{1,2\}$ and $\displaystyle \partial (A)\cap \partial (B)=\emptyset$ .