Definition:Topological Isomorphism

Definition
Let $K$ be a topological field.

Let $\struct {X, \tau_X}$ and $\struct {Y, \tau_Y}$ be topological vector spaces over $K$.

Let $T : X \to Y$ be a linear transformation.

We say that $T$ is a topological isomorphism $T$ is a linear isomorphism and a homeomorphism.