Definition:Topological Property

Let $$P$$ be a property that can sensibly hold for a topological space.

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.

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