Homeomorphism

Set

 context $\langle X,\mathcal{T}_X\rangle, \langle Y,\mathcal{T}_Y\rangle$ … topological spaces definiendum $f\in$ it inclusion $f$ … bijection, continuous postulate $f^{-1}$ … continuous

Discussion

A homeomorphism is a bijection which is continuous in both directions.

Reference

Wikipedia: Homeomorphism