Descriptive Topology in Selected Topics of Functional Analysis (Developments in Mathematics, Band 24) - Softcover

Über die Autorin bzw. den Autor

Jerzy K¿kol is Full Professor of Mathematics at the Adam Mickiewicz University of Poznä (Poland). His research is strongly connected with functional analysis, infinite-dimensional and descriptive topology, and applications of topological methods in functional analysis. He published over 180 research papers, mainly in functional analysis and (descriptive) topology. In 1989/91 he was a scholarship holder of the Alexander von Humboldt foundation, which he carried out at the Universities of Munich and Saarbrucken. He conducted scientific research as a visiting professor at several universities in US (New York, Gainesville and Grand Forks, among others) and in Spain (Valencia, Murcia). Since 2005 he has been a member of the Spanish Royal Academy of Sciences. Wieslaw Kubi¿ is Full Professor of Mathematics, currently a Researcher in the Czech Academy of Sciences, Prague, Czechia, and also Professor at the Cardinal Stefan Wyszynski University in Warsaw, Poland. His research spans several areas of pure mathematics: set theory, category theory, topology, and functional analysis---aiming at developing generic mathematical structures. He has published over 60 research articles, and is a co-author of the first edition of the current monograph. Prof. Kubi¿ is currently leading a prestigious five-year Excellence in Basic Research Grant Project EXPRO, awarded by the Czech Science Foundation. Manuel López-Pellicer was Full Professor of Mathematics at the Polytechnic University of Valencia (Spain) until 2015 and since then he is Professor Emeritus. His research is mainly connected with Functional Analysis, General Topology and applications of topological methods in functional analysis, with over 120 publications. He is a coauthor of the monographs "Metrizable barrelled spaces" (Longman 1995) and of the first edition of the current monograph "Descriptive Topology in Selected Topics of Functional Analysis" (Springer 2011). Since 1998 he is a member of the Royal Academy of Sciences of Spain, being since 2004 editor-in-chief of its Mathematical Journal, with acronym name RACSAM. Damian Sobota is a senior postdoc researcher at the Kurt Gödel Research Center for Mathematical Logic at the University of Vienna, where he has worked since finishing his PhD thesis at the Institute of Mathematics of the Polish Academy of Sciences in 2016. His research interests mostly concern applications of forcing and infinitary combinatorics to problems arising in Banach space theory and measure theory. He is an author or co-author of over 20 research papers.

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A large mathematical community throughout the world actively works in functional analysis and uses profound techniques from topology. As the first monograph to approach the topic of topological vector spaces from the perspective of descriptive topology, this work provides also new insights into the connections between the topological properties of linear function spaces and their role in functional analysis.

Descriptive Topology in Selected Topics of Functional Analysis is a self-contained volume that applies recent developments and classical results in descriptive topology to study the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Fréchet spaces, LF-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in distribution theory, differential equations, complex analysis, and various other areas of functional analysis.

Written by three experts in the field, this book is a treasure trove for researchers and graduate students studying the interplay among the areas of point-set and descriptive topology, modern analysis, set theory, topological vector spaces and Banach spaces, and continuous function spaces. Moreover, it will serve as a reference for present and future work done in this area and could serve as a valuable supplement to advanced graduate courses in functional analysis, set-theoretic topology, or the theory of function spaces.