Baire measurable solutions of a generalized Gołąb–Schinzel equation

J. Brzdęk [1] characterized Baire measurable solutions $f:X\to K$ of the functional equation $$f(x+f(x{)}^{n}y)=f(x)f(y)$$ under the assumption that $X$ is a Fréchet space over the field $K$ of real or complex numbers and $n$ is a positive integer. We prove that his result holds even if $X$ is a linear topological space over $K$; i.e. completeness and metrizability are not necessary.