orbit

Given a space X let $\mathcal H(X)$ stand for the group of autohomeomorphisms of X. If a point $p \in X$ is fixed, then $\{h(p) \in X: h \in \mathcal H(X)\}$ is called an orbit of p. Orbits of points of X either are mutually disjoint or coincide, and their union is the whole X.