The trivial loop is the loop that takes every point to its basepoint. Formally, if 
is a topological space
and 
, the trivial loop based at 
is the map ![L:[0,1]->X](/images/equations/TrivialLoop/Inline4.svg)
given by 
for all ![z in [0,1]](/images/equations/TrivialLoop/Inline6.svg)
.
Trivial Loop
See also
LoopThis entry contributed by John Renze
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Cite this as:
Weisstein, Eric W., with contributions by John Renze. "Trivial Loop." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TrivialLoop.html