Definition:Continuous Invariant

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

Suppose that whenever $P \left({T \ }\right)$ holds, then so does $P \left({T'}\right)$, where:
 * $T$ and $T'$ are topological spaces;
 * $\phi \left({T}\right) = T'$ where $\phi$ is a continuous mapping from $T$ to $T'$.

Then $P$ is known as a continuous invariant.

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

Also see

 * Topological property


 * Open invariant
 * Closed invariant