# General Topology/Pointed spaces and support

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**Definition (pointed topological space)**:

A **pointed topological space** is a pair where is a topological space and .

**Definition (morphism of pointed topological spaces)**:

A **morphism of pointed topological spaces** , and is a continuous function such that .

**Definition (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.