In mathematics, a pointed set is a set X with a distinguished basepoint x₀ in X. Maps of pointed sets (based maps) are functions preserving basepoints, i.e. a map f : X → Y such that f(x₀) = y₀. This is usually denoted

f : (X, x₀) → (Y, y₀).

Pointed sets may be regarded as a rather simple algebraic structure. In the sense of universal algebra, they are structures with a single nullary operation which picks out the basepoint.

See also

• pointed space

Set theory | Abstract algebra