Let $T_0 = (X, \mathcal{T}_0)$ and $T_1 = (X, \mathcal{T}_1)$ each be a D1106: Topological space.

Let $I : X \to X$ be an D440: Identity map on $X$.

Let $I : X \to X$ be an D440: Identity map on $X$.

Then

(1) | If $\mathcal{T}_1 \subseteq \mathcal{T}_0$, then $I$ is a D55: Continuous map with respect to $T_0$ and $T_1$ |

(2) | If $T_0 = T_1$, then $I$ is a D55: Continuous map with respect to $T_0$ |