  By the {\em Suslinian number} $\Sln(X)$ of a continuum $X$ we understand the
smallest cardinal number $\kappa$ such that $X$ contains no disjoint family
$\C$ of non-degenerate subcontinua of size $|\C|\ge\kappa$. For a compact space
$X$, $\Sln(X)$ is the smallest Suslinian number of a continuum which contains a
homeomorphic copy of $X$. Our principal result asserts that each compact space
$X$ has weight $\le\Sln(X)^+$ and is the limit of an inverse well-ordered
spectrum of length $\le \Sln(X)^+$, consisting of compacta with weight
$\le\Sln(X)$ and monotone bonding maps. Moreover, $w(X)\le\Sln(X)$ if no
$\Sln(X)^+$-Suslin tree exists. This implies that under the Suslin Hypothesis
all Suslinian continua are metrizable, which answers a question of
\cite{DNTTT1}. On the other hand, the negation of the Suslin Hypothesis is
equivalent to the existence of a hereditarily separable non-metrizable
Suslinian continuum. If $X$ is a continuum with $\Sln(X)<2^{\aleph_0}$, then
$X$ is 1-dimensional, has rim-weight $\le\Sln(X)$ and weight $w(X)\ge\Sln(X)$.
Our main tool is the inequality $w(X)\le\Sln(X)\cdot w(f(X))$ holding for any
light map $f:X\to Y$.

General Topology