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.
Comparing topologies on linearly recursive sequences
El Kaoutit, Laiachi;Saracco, Paolo
2019-01-01
Abstract
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.
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