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

For a topological flow $(V,\varphi )$ - i.e., $V$ is a linearly compact vector space and $\varphi$ a continuous endomorphism of $V$ - we gain a deep understanding of the relationship between $(V,\varphi )$ and the Bernoulli shift: a topological flow $(V,\varphi )$ is essentially a product of one-dimensional left Bernoulli shifts as many as ${\mathrm{e}\mathrm{n}\mathrm{t}}^{\ast }(V,\varphi )$ 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 $(V,\varphi )$. 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.