In this paper we give an answer to Furstenberg’s problem on topological disjointness. Namely, we show that a transitive system
$(X,T)$
is disjoint from all minimal systems if and only if
$(X,T)$
is weakly mixing and there is some countable dense subset
$D$
of
$X$
such that for any minimal system
$(Y,S)$
, any point
$y\in Y$
and any open neighbourhood
$V$
of
$y$
, and for any non-empty open subset
$U\subset X$
, there is
$x\in D\cap U$
such that
$\{n\in \mathbb{Z}_{+}:T^{n}x\in U,S^{n}y\in V\}$
is syndetic. Some characterization for the general case is also given. By way of application we show that if a transitive system
$(X,T)$
is disjoint from all minimal systems, then so are
$(X^{n},T^{(n)})$
and
$(X,T^{n})$
for any
$n\in \mathbb{N}$
. It turns out that a transitive system
$(X,T)$
is disjoint from all minimal systems if and only if the hyperspace system
$(K(X),T_{K})$
is disjoint from all minimal systems.