I apologize in advance if this question is too elementary for MO. I am new to the field of algebraic geometry.
I am dealing with a (real) algebraic variety $V$ of (Krull) dimension $n$. I keep reading that $V$ can be decomposed into differentiable manifolds of dimensions $0, 1, ..., n$.
While this seems plausible I could not find this statement in the literature. Is it true? I would also be glad about a reference.