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 preserved under homeomorphism.

Also see

• Continuous invariant
• Open invariant
• Closed invariant

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 1$: Functions