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