Existence of Non-Locally Connected Space where Components and Quasicomponents are Equal

Theorem
There exists at least one example of a topological space which is not locally connected, but whose components and quasicomponents are equal.

Proof
Let $T$ be the Arens-Fort space.

From Arens-Fort Space is not Locally Connected, $T$ is not a locally connected space.

The result follows from Components and Quasicomponents of Arens-Fort Space are Equal.