0
$\begingroup$

How does one show that any open interval in n-dimensional Euclidean space is connected?

This is homework, and I have been stuck on it for a few hours now. Seems like it should be easy, but I can't get a proof that I am comfortable with.

  • 0
    @Roig Yes, that was a much easier proof for me.2010-11-18

2 Answers 2

3

OK. This is a basic result which states that Cartesian product of connected sets are connected. You may look here for the proof:

0

Can you show that an interval is connected in $\mathbb{R}$? Then can you say (a,b) is connected to (c,b) is connected to (c,d)?