Products of ANR-homology manifolds (Ex)

Let $M$$<wikitex>; Let $M$ and $N$ be $\mathrm{ANR}$-homology manifolds of dimension $\ge 5$ having the (DDP). Show that $M \times N$ is a topological closed manifold if and only if both $M$ and $N$ are a closed topological manifolds. </wikitex> [[Category:Exercises]] [[Category:Exercises without solution]]M$ and $N$$N$ be $\mathrm{ANR}$$\mathrm{ANR}$-homology manifolds of dimension $\ge 5$$\ge 5$ having the (DDP). Show that $M \times N$$M \times N$ is a topological closed manifold if and only if both $M$$M$ and $N$$N$ are a closed topological manifolds.