This self-contained volume applies recent developments and classical results to study the classes of infinite-dimensional topological vector spaces in functional analysis.

"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on 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 functional analysis in distribution theory, differential equations, complex analysis, and various other analytical settings. This monograph provides new insights into the connections between the topological properties of linear function spaces and their applications in functional analysis.

Presents numerous results that have previously only appeared in journal publications Includes several newly developed and unpublished results Can serve a supplementary text in course focusing on selected topics in functional analysis, set topology, or the theory or functional spaces This is the first monograph to approach the topic of linear functional equations from the perspective of descriptive topology Includes supplementary material: sn.pub/extras

Autorentext

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.

Klappentext

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.

Inhalt

Preface.- 1. Overview.- 2. Elementary Facts about Baire and Baire-Type Spaces.- 3. K-analytic and quasi-Suslin Spaces.- 4. Web-Compact Spaces and Angelic Theorems.- 5. Strongly Web-Compact Spaces and a Closed Graph Theorem.- 6. Weakly Analytic Spaces.- 7. K-analytic Baire Spaces.- 8. A Three-Space Property for Analytic Spaces.- 9. K-analytic and Analytic Spaces C p (X) .- 10. Precompact sets in (LM) -Spaces and Dual Metric Spaces.- 11. Metrizability of Compact Sets in the Class G.- 12. Weakly Realcompact Locally Convex Spaces.- 13. Corson's Propery (C) and tightness.- 14. Fréchet-Urysohn Spaces and Groups.- 15. Sequential Properties in the Class G.- 16. Tightness and Distinguished Fréchet Spaces.- 17. Banach Spaces with Many Projections.- 18. Spaces of Continuous Functions Over Compact Lines.- 19. Compact Spaces Generated by Retractions.- 20. Complementably Universival Banach Space.- Index.