Identity Mapping is Homeomorphism

Theorem
Let $T$ be a topological space.

The identity mapping $I_T: T \to T$ defined as:
 * $\forall x \in T: I_T \left({x}\right) = x$

is a homeomorphism.

Proof
We have that the Identity Mapping is a Bijection.

We also have that the Identity Mapping is Continuous.

Hence, by definition of homeomorphism, $I_T$ is a homeomorphism.