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Open Mathematics: Topical Issue on Topological and algebraic genericity in Infinite Dimensional Spaces

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Juan B. Seoane Sepúlveda, Universidad Complutense de Madrid and and ICMAT, Spain

Email: jseoane@ucm.es


Vector spaces and linear algebras are elegant mathematical structures, which at first glance seem to be forbidden to families of strange objects. This, however, is far from the truth. In recent years many researchers have constructed large algebraic structures (linear spaces, closed subspaces, algebras, etc.) of mathematical objects enjoying certain, a priori, exceptional properties. Over the last decade, this topic has attracted the attention of the mathematical community, with over 100 papers being published, most of them in highly ranked mathematical journals.

In a nutshell, the main idea is as follows. Let M be a subset of some topological vector space X. Then it is called lineable if M ∪ {0} contains an infinite dimensional linear space, and it is called spaceable if this linear space can even be chosen to be closed in X. Moreover, the very recent publication of a survey paper and a monograph dedicated to this topic witness to the growing interest in this area.

An important aspect of lineability and spaceability is that it links, and draws from, many different areas of mathematics, from Real and Complex Analysis passing through Set Theory and Linear and Multilinear Algebra, to Operator Theory, Topology, Measure Theory, and even Probability Theory. Any lineability results within the previous scope of areas and fields will be welcome to this special issue.

Primary: 15A03, 02K, 46E10, 46E15, 47A16.
Secondary: 26B05, 28A20, 47A16, 47L05, 54.