A D18: Map $f : X \to Y$ is a homeomorphism from $T_X$ to $T_Y$ if and only if
| (1) | $f$ is a D55: Continuous map from $T_X$ to $T_Y$ |
| (2) | $f$ is an D976: Invertible map with an D216: Inverse map $f^{-1} : Y \to X$ |
| (3) | $f^{-1}$ is a D55: Continuous map from $T_Y$ to $T_X$ |