PlanetPhysics/Birkhoff Kakutani Theorem
Jump to navigation
Jump to search
Birkhoff-Kakutani theorem[edit | edit source]
\begin{theorem}
A topological group is metrizable if and only if is Hausdorff and the identity of has a countable neighborhood basis. Furthermore, if G is metrizable , then admits a compatible metric which is left-invariant, that is, a right-invariant metric also exists under these conditions. \end{theorem}
All Sources[edit | edit source]
References[edit | edit source]
- ↑ Howard Becker, Alexander S. Kechris. 1996. The Descriptive Set Theory of Polish Group Actions. (London Mathematical Society Lecture Note Series) , Cambridge University Press: Cambridge, UK, p.14.