Tell me more ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.
up vote 0 down vote favorite

Consider two $n$-connected sets $U,V\in \mathbb{R}^m$. What is the minimal $m$ such there exist $U,V$ such that $U\cap V$ is not connected? $n$-connected?

share|improve this question
I don't quite understand. Do you mean to ask "What is the smallest $m$ such that there are two $n$-connected subsets $U,V\subset\mathbb R^m$ whose intersection is disconnected/not $n$-connected?" You can have two spaces that are contractible, deformed balls for instance, whose intersection is not even connected. Think of two sets shaped like the letter U that intersect only at the extremities of the U. You get two path components this way. Am I misunderstanding your question? – Olivier Bégassat Jul 20 '12 at 23:24
@OlivierBégassat Yes, you understood me. I'm still getting a hang for algebraic topology. – pre-kidney Jul 20 '12 at 23:36
I think you need to specify the $n$ at here. For arbitrarily numbers this can be as bad as you wish. – user32240 Jul 21 '12 at 6:48

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.