Linear dynamical system: compactness theorem (Q1333855)

Let \(k\) be a complete valued field. ``A Willems (resp. Laurent-Willems) module is a topological linear space (over \(k\)) together with a linear continuous endomorphism (resp. automorphism) of this space which is isomorphic to a closed linear time-invariant subspace in \((k^ q)^{\mathbb{Z}_+}\) (resp. \((k^q)^{\mathbb{Z}}\)) together with the left-shift operator.'' For the above `abstract version' of behaviour the author defines a compact topology on the subset of behaviour having a fixed input number and MacMillan degree. A continuous bijective parametrization of this set is also presented.