Why is log(n) a space-constructible function? According to "Constructible function", Wikipedia:


  In complexity theory, a time-constructible function is a function f from natural numbers to natural numbers with the property that f(n) can be constructed from n by a Turing machine in the time of order f(n).


But $\log\left(n\right)$ doesn't map onto natural numbers but to real numbers.

Why is $\log\left(n\right)$ nevertheless a space-constructible function?
Because when we write $\log n$ it's either in a context where it doesn't matter (e.g. Landau bounds) or with the implicit meaning of $\lfloor \log n \rfloor$ or $\lceil \log n \rceil$.

It certainly doesn't make sense to talk about constructible functions with real range, I would assume your source is talking about $\lfloor \log n \rfloor$ or $\lceil \log n \rceil$.