In *Locally Presentable and Accessible Categories*, page 12 (10), 

> A topological space is finitely presentable in $\mathbf{Top}$, the category of topological spaces and continuous functions, iff it is finite and discrete.

But the explanation after this sentence makes little sense to me. In particular, I want a rigorous proof that every finitely presentable object in $\mathbf{Top}$ is finite and discrete.