Intrinsic entropy for generalized quasimetric semilattices

摘要

We introduce the notion of intrinsic semilattice entropy h̃ in the category ℒqm of generalized quasimetric semilattices and contractive homomorphisms. By using appropriate categories ? and functors F:?→ℒqm, we find specific known entropies h̃? on ? as intrinsic functorial entropies, that is, as h̃?=h̃∘F. These entropies are the intrinsic algebraic entropy, the algebraic and the topological entropies for locally linearly compact vector spaces, the topological entropy for totally disconnected locally compact groups and the algebraic entropy for compactly covered locally compact abelian groups.