1. ## Relationship of Boundaries

,.,just wondering..

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

2. ## Re: Relationship of Boundaries

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 $\displaystyle \partial(a,b)\cap\partial(b,c)$?

3. ## 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

4. ## Re: Relationship of Boundaries

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 $\displaystyle \partial (A)\cap \partial (B)=\emptyset$ .