0
$\begingroup$

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 $\vert K\vert$.

  • 0
    What if the two polyhedra touch each other's faces?2011-05-10
  • 0
    What does |X| is the polyhedron of X mean?2011-05-10
  • 0
    @M.B. : I've edited the post for explanation.2011-05-10

1 Answers 1