General Topology/Pointed spaces and support

pointed topological space A pointed topological space is a pair where is a topological space and . morphism of pointed topological spaces A morphism of pointed topological spaces , and is a continuous function such that . support Let be a continuous map, where is a distinguished point. Then the support of is defined to be . Often, is a topological magma with identity, and is the identity. For instance, and would be a possibility.