1992/08/20 by Vladimir Pestov, Vladimir G. Pestov, Pestov, Vladimir G. · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Operator Algebras (math.OA) #funct-an #math.OA
paper · pdf · doi:10.48550/arxiv.funct-an/9208001
35 pages, AmS TeX 2.1
arxiv created 1992/08/20 · openalex publication_date 1992/08/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We survey the present trends in theory of universal arrows to forgetful functors from various categories of topological algebra and functional analysis to categories of topology and topological algebra. Among them are free topological groups, free locally convex spaces, free Banach-Lie algebras, and much more. An accent is put on relationship of those constructions with other areas of mathematics and their possible applications. A number of open problems is discussed; some of them belong to universal arrow theory, and others may hopefully become amenable to methods of this theory.