Hi all!(adsbygoogle = window.adsbygoogle || []).push({});

I am reading a book on Classical Electrodynamics (Hehl and Obukhov, Foundations of Classical Electrodynamics, Birkhauser, 2003). In this manual I found the following statement:

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Consider a 4-dimensional differentiable manifold which is:

-connected (every 2 points are connected by continuous curve)

-Hausdorff (http://en.wikipedia.org/wiki/Hausdorff_space#Definitions)

-orientable (http://en.wikipedia.org/wiki/Orientability#Orientation_of_differential_manifolds)

-paracompact (manifold covered by finite number of coordinate charts)

This manifold always has a foliation by 3-dimensional hypersurfaces (each hypersurface is a hypersurface of constant "time").

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Does anyone know another reference which confirms this statement? In other words, do you know why a connected Hausdorff orientable paracompact manifold always has such foliation?

Any help is massively appreciated!

Cheers!

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# Foliation of 4-dimensional connected Hausdorff orientable paracompact manifold

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