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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?

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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 $n < 4$).

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  • $\begingroup$ Can you tell me What is embedding, tell me in simple manner. If possible through real world example. $\endgroup$
    – SHREE6174
    Jan 15, 2015 at 16:26
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    $\begingroup$ An embedding of $K$ into $\mathbb{R}^4$ is a way of considering the Klein bottle inside of $\mathbb{R}^4$ without self-intersections. The usual picture in $\mathbb{R}^3$ has self-intersections, so it isn't an embedding, but rather an immersion. $\endgroup$ Jan 15, 2015 at 16:29

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