Why is a klein Bottle 4-D?

Question

I am wondering why a Klein Bottle is 4-D. Can anybody tell me how it is possible? I can represent the Klein Bottle in 3-D. Then how can it be 4-D?

What is immersion? What is embedding? Basically, Here I got the concept. And also I've watched some videos in youtube about construction from rectangle strip. Can anybody explain it in a simpler way?

Answer 1

The Klein bottle is a surface, a two-dimensional manifold, but it can be embedded in $\mathbb{R}^4$ (but not $\mathbb{R}^n$ for any $n < 4$).