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
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