I've met a problem in M.A.Armstrong's Basic Topology.
If $K$ and $L$ are complexes in $\mathbb{E}^n$, show that $\vert K\vert\cap\vert L\vert$ is a polyhedron.
where $\vert K\vert$ and $\vert L\vert$ are the polyhedron of $K$ and $L$.
I think it's not hard to imagine this statement. But I can't find a formal proof for this.
Can you please help? Thank you.
EDIT: The definition of a polyhedron in Basic Topology is:
... the union of the simplexes which make up a particular complex is a subset of a euclidean space, and can therefore be made into a topological space by giving it the subspace topology. A complex $K$, when regarded in this way as a topological space, is called a polyhedron and written $\vert K\vert$.