Comparing topologies on linearly recursive sequences - El Kaoutit, Laiachi (Ars mathematica contemporanea, 2019)
The space of linearly recursive sequences of complex numbers admits two distinguished topologies. Namely, the adic topology induced by the ideal of those sequences whose first term is 0 and the topology induced from the Krull topology on the space of complex power series via a suitable embedding. We show that these topologies are not equivalent.
Keywords: adic topologies; adične topologije; Hopf algebras; Hopfove algebre; linearly recursive sequences; linearno rekurzivna zaporedja; potenčne vrste; power series