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{{Short description|Concept in topology}}
In mathematics, '''topological complexity''' of a [[topological space]] ''X'' (also denoted by TC(''X'')) is a [[topological invariant]] closely connected to the [[motion planning]] problem{{elucidate|date=July 2012}}, introduced by Michael Farber in 2003.
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*If <math>F(\R^m,n)</math> is the [[Configuration space (mathematics)|configuration space]] of ''n'' distinct points in the Euclidean ''m''-space, then
::<math>TC(F(\R^m,n))=\begin{cases} 2n-1 & \mathrm{for\,\, {\it m}\,\, odd} \\ 2n-2 & \mathrm{for\,\, {\it m}\,\, even.} \end{cases}</math>
*The topological complexity of the [[Klein bottle]] is 5.<ref>{{Cite
==References==
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