  We study the following optimal $L^2$ extension problem of openness type:
given a complex manifold $M$, a closed subvariety $S\subset M$ and a
holomorphic vector bundle $E\rightarrow M$, for any $L^2$ holomorphic section
$f$ defined on some open neighborhood $U$ of $S$, find an $L^2$ holomorphic
section $F$ on $M$ such that $F|_S = f|_S$, and the $L^2$ norm of $F$ on $M$ is
optimally controlled by the $L^2$ norm of $f$ on $U$.
  Answering the above problem, we prove an optimal $L^2$ extension theorem of
openness type on weakly pseudoconvex K\"ahler manifolds, which generalizes a
couple of known results on such a problem. Moreover, we prove a product
property for certain minimal $L^2$ extensions and give an alternative proof to
a version of the above $L^2$ extension theorem. We also present some
applications to the usual optimal $L^2$ extension problem and the equality part
of Suita's conjecture.
