Special Numbers: update

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This post is a continuation of my earlier post: Special Numbers

Four (4)

This is the only euclidean space with properties different from other n-dimensional euclidean spaces. For example, there are smooth 4-manifolds which are homeomorphic but not diffeomorphic.  Put differently, for any dimension except four there is only one differentiable structure on the space underlying the Euclidean space of that dimension. For a discussion in this direction see this article by Liviu Nicolaescu. For other special properties of 4-dimesnions read Wikipedia article on 4-manifold.
Thanks to Dr. Ritwik Mukherjee for explaining this fact about four-space.

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  1. Pingback: Dimension clarification | Gaurish4Math

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