Let $G$ be a topological group acting continuously on a topological space $X$ by homeomorphisms. That is, the action map $G \times X \to X$, $(g, x) \mapsto g \cdot x$, is continuous, and for each $g \in G$, the map $x \mapsto g \cdot x$ is a homeomorphism. Then the quotient map $\pi: X \to X/G$ is open.