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 if and only if $T$ is a linear isomorphism and a homeomorphism.

Sources

• 1963: John L. Kelley and Isaac Namioka: Linear Topological Spaces ... (previous) ... (next): $5$: Linear Topological Spaces, Linear Functions, Quotients, and Products