Answer to Question #211543 in Real Analysis for Matome

Question

Let f : M → Y be a homeomorphism and O an open subset of M. Explain

concisely in no more than two lines of text why f(O) is an open set.

Answer 1

Since function is homeomorphism, M is mapped one to one and onto Y. This means a function of O which is an open subset is an open set since Y takes the identity in M.