In mathematics, a pointed space is a topological space X with a distinguished basepoint x0 in X. Maps of pointed spaces (based maps) are continuous maps preserving basepoints, i.e. a continuous map f : X → Y such that f(x0) = y0. This is usually denoted
- f : (X, x0) → (Y, y0).
Pointed spaces are important in algebraic topology, particularly in homotopy theory, where many constructions, such as the fundamental group, depend on a choice of basepoint.
The pointed set concept is less important; it is anyway the case of a pointed discrete space.
Read more about Pointed Space: Category of Pointed Spaces, Operations On Pointed Spaces
Famous quotes containing the words pointed and/or space:
“Be sure that it is not you that is mortal, but only your body. For that man whom your outward form reveals is not yourself; the spirit is the true self, not that physical figure which can be pointed out by your finger.”
—Marcus Tullius Cicero (106–43 B.C.)
“There is commonly sufficient space about us. Our horizon is never quite at our elbows.”
—Henry David Thoreau (1817–1862)