Hi

Let be a group, and consider a group action of on a topological space Then the quotient map is open: indeed, since translations (given a maps in like ) are homeomorphisms, given an open set of is a union of open sets (the image of an open set under a homeomorphism is an open set) thus is open and by quotient topology definition, is open.

Ok, that's a more general case, but it can give you an idea to solve your problem, the chosen group being particular.