Definition:Continuous Invariant

Definition
Let $P$ be a property whose domain is the set of all topological spaces.

Suppose that whenever $\map P T$ holds, then so does $\map P {T'}$, where:
 * $T$ and $T'$ are topological spaces
 * $\phi: T \to T'$ is a continuous mapping from $T$ to $T'$
 * $\phi \sqbrk T = T'$, where $\phi \sqbrk T$ denotes the image of $\phi$.

Then $P$ is a continuous invariant.

Loosely, a continuous invariant is a property which is preserved under a continuous mapping.

Also see

 * Definition:Topological Property


 * Definition:Open Invariant
 * Definition:Closed Invariant