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:
“See! those fiendish lineaments graven on the darkness, the writhed lip of scorn, the mockery of that living eye, the pointed finger, touching the sore place in your heart! Do you remember any act of enormous folly, at which you would blush, even in the remotest cavern of the earth? Then recognize your Shame.”
—Nathaniel Hawthorne (1804–1864)
“Oh, my. I’d forgotten how much I hate space travel.”
—George Lucas (b. 1944)