Definition:Topological Property

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 which are homeomorphic.

Then $$P$$ is known as a topological property or a topological invariant.

Loosely, a topological property is one which is conserved under homeomorphism.