\begin{definition}[Definition:Closed Invariant]
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 mapping from $T$ to $T'$
:$\phi \sqbrk T = T'$, where $\phi \sqbrk T$ denotes the image of $\phi$
:$T'$ is a closed set.
Then $P$ is a '''closed invariant'''.
Loosely, an closed invariant is a property which is preserved in the closed image of a mapping.
\end{definition}