The first homotopy group, or fundamental group, of a (path connected) topological space thus begins with continuous maps from a pointed circle to the pointed space , where maps from one pair to another map into . These maps (or equivalently, closed curves) are grouped together into equivalence classes based on homotopy (keeping the "base point" fixed), so that two maps are in the same class if they are homotopic. Just as one point is distinguished, so one class is distinguished: all maps (or curves) homotopic to the constant map are called null homotopic. The classes become an abstract algebraic group with the introduction of addition, defined via an "equator pinch". This pinch maps the equator of a pointed sphere (here a circle) to the distinguished point, producing a "bouquet of spheres" — two pointed spheres joined at their distinguished point. The two maps to be added map the upper and lower spheres separately, agreeing on the distinguished point, and composition with the pinch gives the sum map.