  Clearly, a generalized inverse limit of metrizable spaces indexed by $\mathbb
N$ is metrizable, as it is a subspace of a countable product of metrizable
spaces. The authors previously showed that all idempotent, upper
semi-continuous, surjective, continuum-valued bonding functions on $[0,1]$
(besides the identity) satisfy a certain Condition $\Gamma$; it follows that
only in trivial cases can a generalized inverse limit of copies of ([0,1])
indexed by an uncountable ordinal be metrizable. The authors show that
Condition $\Gamma$ is in fact guaranteed by much weaker criteria, proving a
more general metrizability theorem for certain Mahavier Products.
