Pointed space
In mathematics, a pointed space is a topological space with a distinguished point, the basepoint. Maps of pointed spaces (based maps) are continuous maps preserving basepoints, i.e., a map f between a pointed space X with basepoint x0 and a pointed space Y with basepoint y0 is a based map if it is continuous with respect to the topologies of X and Y and if f(x0) = y0. This is usually denoted