  Theorem A. Let $M^n$ denote a closed Riemannian manifold with nonpositive
sectional curvature and let $\tilde M^n$ be the universal cover of $M^n$ with
the lifted metric. Suppose that the universal cover $\tilde M^n$ contains no
totally geodesic embedded Euclidean plane $\mathbb{R}^2$ (i.e., $M^n$ is a
visibility manifold). Then Gromov's simplicial volume $\| M^n \|$ is non-zero.
Consequently, $M^n$ is non-collapsible while keeping Ricci curvature bounded
from below. More precisely, if $Ric_g \ge -(n-1)$, then $vol(M^n, g) \ge
\frac{1}{(n-1)^n n!} \| M^n \| > 0.
  Theorem B. (Perelman) Let $M^3$ be a closed a-spherical 3-manifold ($K(\pi,
1)$-space) with the fundamental group $\Gamma$. Suppose that $\Gamma$ contains
no subgroups isomorphic to $\mathbb{Z}\oplus \mathbb{Z}$. Then $M^3$ is
diffeomorphic to a compact quotient of real hyperbolic space $\mathbb{H}^3$,
i.e., $M^3 \equiv \mathbb{H}^3/\Gamma$. Consequently, $MinVol(M^3) \ge {1/24}\|
M^3 \| > 0$.
  Minimal volume and simplicial norm of all other compact 3-manifolds without
boundary and {\it singular} spaces will also be discussed.
