Toposes Pour Les Vraiment Nuls (warning: PDF). Actually in English, in spite of the title. Well, I say “English”:

In a topological development, one would follow this with a definition of the

usual topology on the set R of real numbers. If q is rational, let us write (q, ?) for the set of reals x for which q ? Lx (i.e. q < x), and (-?, q) for the set of reals x for which q ? Rx. These are defined to be "subbasic open" subsets of R, and in general the open subsets are those that can be expressed as unions of finite intersections of subbasics. (The intersection (-?,q+?)?(q-?,?) gives the rational open ball B?(q), the set of reals strictly between q-? and q+?, and the open sets are usually characterized as the unions of these.)

Dedekind cuts still do my head in.