The corank of a flow over the category of linearly compact vector spaces

For a topological flow (V,ϕ) - i.e., V is a linearly compact vector space and ϕ a continuous endomorphism of V - we gain a deep understanding of the relationship between (V,ϕ) and the Bernoulli shift: a topological flow (V,ϕ) is essentially a product of one-dimensional left Bernoulli shifts as many as ent⁎(V,ϕ) counts. This novel comprehension brings us to introduce a notion of corank for topological flows designed for coinciding with the value of the topological entropy of (V,ϕ). As an application, we provide an alternative proof of the so-called Bridge Theorem for locally linearly compact vector spaces connecting the topological entropy to the algebraic entropy by means of Lefschetz duality.