A continuous map 
between topological spaces is said to be null-homotopic if it is homotopic
to a constant map.
If a space 
has the property that 
,
the identity map on 
,
is null-homotopic, then 
is contractible.
Null-Homotopic
This entry contributed by Rasmus Hedegaard
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Hedegaard, Rasmus. "Null-Homotopic." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Null-Homotopic.html