I've encountered a definition in several papers, but literally none of them define the term. They all instead reference a book by Menger that has never been printed in English. The term is "rim-type" of a topological space; the context I'm running into it in is the theory of curves/one-dimensional spaces.

A curve $X$ is a one-dimensional topological space, and a curve is *rational* if there's a basis $\lbrace U_\beta \rbrace$ such that $\partial(U_\beta)$ is countable for all $\beta$. Then they say that a rational curve has *rim-type* $\alpha$ if every such boundary $\partial(U_\beta)$ has an $\alpha$-th derivative of zero, and $\alpha$ is minimal among ordinals with this property.

So what I really need to know is what is meant by "derivative" here. I do own the Menger book, because at one point I considered translating it as a good deed. My vague impression from looking at this section (pp. 291-297 of Kurventheorie) is that it is just some set theory definition involving transfinite induction.

Is the "derivative" of a countable topological space just what remains after removing its isolated points? Or is it more complicated? If relevant, my spaces will be compact metric spaces, so whatever the nicest definition for that case is would be best. My googling skills weren't good enough to get past all the calculus videos when I tried to search for what the derivative of a countable set is.

Thanks!