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 given by for all .
Trivial Loop
See also
LoopThis entry contributed by John Renze
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Renze, John. "Trivial Loop." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/TrivialLoop.html