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Topologically Algebraic Algebras
Mediterranean Journal of Mathematics, 2004Let \(A\) be a complex topological algebra and \(H(\mathbb{C})\) the algebra of all complex-valued entire functions. An element \(x\) in \(A\) is said to be topologically algebraic if all entire functions operate in \(A\) at the point \(x\) and if there exists a nonzero entire function \(f\) in \(H(\mathbb{C})\) such that \(f(x)=0\).
Choukri, Rachid, Attioui, Abdelbaki
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Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology
International Conference on Learning Representations, 2018While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been developed.
Bastian Alexander Rieck +6 more
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HYPERGROUP ALGEBRAS AS TOPOLOGICAL ALGEBRAS
Bulletin of the Australian Mathematical Society, 2014AbstractLet$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}K$be a locally compact hypergroup endowed with a left Haar measure and let$L^1(K)$be the usual Lebesgue space of$K$with respect ...
Maghsoudi, S., Seoane-Sepúlveda, J. B.
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Stable Algebraic Topology and Stable Topological Algebra
Bulletin of the London Mathematical Society, 1998The article is essentially the text of a lecture held at the London Mathematical Society. The author gives an overview of the history of stable algebraic topology since the early 1960's.
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Infrasequential Topological Algebras
Canadian Mathematical Bulletin, 1979The notion of sequential topological algebra was introduced by this author and Ng [3], Among a number of results concerning these algebras, we showed that each multiplicative linear functional on a sequentially complete, sequential, locally convex algebra is bounded ([3], Theorem 1). From this it follows that every multiplicative linear functional on a
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Differential forms in algebraic topology
Graduate texts in mathematics, 1982R. Bott, L. Tu
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