  The Hosotani mechanism claims to achieve gauge-symmetry breaking, for
instance $SU(3) \to SU(2)\times U(1)$. To verify this claim, we propose to
monitor the stability of a topological defect stable under a gauge subgroup but
not under the whole gauge group, like a $U(1)$ flux state or monopole in the
case above. We use gauge invariant operators to probe the presence of the
topological defect to avoid any ambiguity introduced by gauge fixing. Our
method also applies to an ordinary gauge-Higgs system.
