A pointed space is a topological space 
together with a choice of a basepoint 
. The notation for a pointed space
is 
. Maps
between two pointed spaces must take basepoints to
basepoints. Pointed spaces are widely used in algebraic
topology, homotopy theory, and topological
K-theory.
Pointed Space
See also
Pointed MapThis entry contributed by John Renze
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References
Bredon, G. Topology and Geometry New York: Springer-Verlag, p. 128, 1993.Referenced on Wolfram|Alpha
Pointed SpaceCite this as:
Weisstein, Eric W., with contributions by John Renze. "Pointed Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PointedSpace.html