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:
“Master the night nor serve the snowman’s brain
That shapes each bushy item of the air
Into a polestar pointed on an icicle.”
—Dylan Thomas (1914–1953)
“The woman’s world ... is shown as a series of limited spaces, with the woman struggling to get free of them. The struggle is what the film is about; what is struggled against is the limited space itself. Consequently, to make its point, the film has to deny itself and suggest it was the struggle that was wrong, not the space.”
—Jeanine Basinger (b. 1936)