Homeomorphism

Not to be confused with "Homomorphism"

Topological Homeomorphism

A topological homeomorphism is bijective map between two topological spaces

$$f:(X,\mathcal{J})\rightarrow(Y,\mathcal{K})$$ where:

1. $$f$$ is bijective
2. $$f$$ is continuous
3. $$f^{-1}$$ is continuous