Natural Topologies on Colombeau Algebras
J. Aragona, R. Fernandez, S. O. Juriaans
TL;DR
This paper introduces natural topologies on Colombeau algebras that align with their algebraic structure, facilitating the application of topological methods to solve PDEs within these algebras.
Contribution
It defines new compatible topologies on Colombeau algebras, extending previous sharp topologies and enabling advanced topological analysis for PDEs.
Findings
Defined natural topologies compatible with algebraic structure
Reduced to Scarpalezos sharp topologies in specific cases
Paves the way for topological PDE methods in Colombeau algebras
Abstract
We define natural topologies on the Colombeau algebras which are compatible with the algebraic structure. These topologies reduces do Scarpalezos sharp topologies when restricted. with this we take a positive step towards topological methods of solving P.D. Equations in Colombeau algebras. Applications will appear elsewhere.
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Taxonomy
TopicsMathematical and Theoretical Analysis · Clinical Reasoning and Diagnostic Skills · Philosophy and History of Science