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.

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

Also known as

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