One useful variant is the homotopy category of pointed spaces. A pointed space means a pair ("X","x") with "X" a topological space and "x" a point in "X", called the base point. The category Top* of pointed spaces has objects the pointed spaces, and a morphism "f": "X" → "Y" is a continuous map that takes the base point of "X" to the base point of "Y". The naive homotopy category of pointed spaces has the same objects, and morphisms are homotopy classes of pointed maps (meaning that the base point remains fixed throughout the homotopy). Finally, the "true" homotopy category of pointed spaces is obtained from the category Top* by inverting the pointed maps that are weak homotopy equivalences.