(a) Let $K, L$ be simplicial complexes, and $f:|K| \rightarrow|L|$ a continuous map. What does it mean to say that $g: K \rightarrow L$ is a simplicial approximation to $f ?$

(b) Define the barycentric subdivision of a simplicial complex $K$, and state the Simplicial Approximation Theorem.

(c) Show that if $g$ is a simplicial approximation to $f$ then $f \simeq|g|$.

(d) Show that the natural inclusion $\left|K^{(1)}\right| \rightarrow|K|$ induces a surjective map on fundamental groups.