Topological Property

Definition (Topological Property)

A property of a space is topological if the property holds for $X$ implies the property holds for any $Y$ where $Y\cong X$.

For example, being Hausdorff is topological. Being bounded for a Metric Space is not topological. From example 1, $(-1,1)\cong \mathbb{R}$, but $\mathbb{R}$ is not bounded.