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 Map
*This 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 Space## Cite this as:

Renze, John. "Pointed Space." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/PointedSpace.html