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
Explore with Wolfram|Alpha
Cite this as:
Renze, John. "Trivial Loop." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TrivialLoop.html