A basepoint is the beginning and ending point of a loop. The fundamental group of a topological space is always with respect to a particular choice of basepoint.
Basepoint
See also
Fundamental Group, LoopThis entry contributed by John Renze
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Renze, John. "Basepoint." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Basepoint.html