Definition:Topological Property

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 which are homeomorphic.

Then $P$ is known as a topological property.

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

Also known as

 * A topological property is also known as a topological invariant.

Also see

 * Definition:Continuous Invariant
 * Definition:Open Invariant
 * Definition:Closed Invariant