Task:Equivalent properties to homeomorphism

Task

Fit the following into the main wiki

Statement

Let $(X,\mathcal{ J })$ and $(Y,\mathcal{ K })$ be topological spaces and let $f:X\rightarrow Y$ be a map. Then:

• If $f$ is a bijective and continuous map, the following are equivalent:
  1. $f$ is a homeomorphism
  2. $f$ is an open map
  3. $f$ is a closed map