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:
“Lord, thy most pointed pleasure take
And stab my spirit broad awake;
Or, Lord, if too obdurate I,
Choose thou, before that spirit die,
A piercing pain, a killing sin,
And to my dead heart run them in!”
—Robert Louis Stevenson (1850–1894)
“Finally she grew quiet, and after that, coherent thought. With this, stalked through her a cold, bloody rage. Hours of this, a period of introspection, a space of retrospection, then a mixture of both. Out of this an awful calm.”
—Zora Neale Hurston (1891–1960)