Why would the category of topological spaces be a balanced category (i.e. monic epimorphisms are isomorphisms)? I've just read on this page that 

For example, $\mathsf {Set}$ (the cateogry of sets), $\mathsf {Grp}$ (the category of groups), and $\mathsf {Top}$ (the category of topological spaces) are all balanced.

(Balanced means that all the monic epimorphisms are isomorphisms).
I clearly understand for $\mathsf{Set}$ and $\mathsf{Grp}$, but isn't this wrong for $\mathsf{Top}$? For instance,
$$f:[0,1[ \longrightarrow S^1 \qquad t \longmapsto e^{2πit}$$
is continuous and bijective but is not an isomorphism in $\mathsf{Top}$. Am I missing something there?
Thank you for your comments!

As it was pointed out in the comments (by Pedro Sánchez Terraf and Rob Arthan), the PlanetMath page is wrong. It is not true that every monic epimorphism in $\sf Top$ is an isomorphism.
Other examples of such morphisms can be found in the category of Hausdorff spaces $\sf Haus$ (looking at the inclusion $\Bbb Q \hookrightarrow \Bbb R$) or in $\sf Ring$ (looking at $\Bbb Z \hookrightarrow \Bbb Q$).
