  We study the existence of solutions to general measure-minimization problems
over topological classes that are stable under localized Lipschitz homotopy,
including the standard Plateau problem without the need for restrictive
assumptions such as orientability or even rectifiability of surfaces. In case
of problems over an open and bounded domain we establish the existence of a
"minimal candidate", obtained as the limit for the local Hausdorff convergence
of a minimizing sequence for which the measure is lower-semicontinuous.
Although we do not give a way to control the topological constraint when taking
limit yet -- except for some examples of topological classes preserving local
separation or for periodic two-dimensional sets -- we prove that this candidate
is an Almgren-minimal set. Thus, using regularity results such as Jean Taylor's
theorem, this could be a way to find solutions to the above minimization
problems under a generic setup in arbitrary dimension and codimension.
