By analogy with the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We study the fundamental properties of this entropy and we prove the Addition Theorem, showing that the topological entropy is additive with respect to short exact sequences. By means of Lefschetz Duality, we connect the topological entropy to the algebraic entropy in a so-called Bridge Theorem
Castellano, I., Giordano Bruno, A. (2019). Topological entropy for locally linearly compact vector spaces. TOPOLOGY AND ITS APPLICATIONS, 252, 112-144 [10.1016/j.topol.2018.11.009].
Topological entropy for locally linearly compact vector spaces
Castellano, I;
2019
Abstract
By analogy with the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We study the fundamental properties of this entropy and we prove the Addition Theorem, showing that the topological entropy is additive with respect to short exact sequences. By means of Lefschetz Duality, we connect the topological entropy to the algebraic entropy in a so-called Bridge Theorem
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