Definition:Topological Property

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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

  • Results about topological properties can be found here.