Duality of Discrete Topological Vector Spaces

2014/10/23 by Ramamonjy Andriamifidisoa, Andriamifidisoa, Ramamonjy
Mathematics · #15A03 #Advanced Topology and Set Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.AC #msc:15A03

paper · pdf · doi:10.48550/arxiv.1410.6324

8 pages

arxiv created 2014/10/23 · openalex publication_date 2014/10/23 · arxiv updated 2014/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a field \ef, the discrete topological vector spaces over \ef are essentially of the form \ef^α where α is an ordinal. With additional appropriate properties, they are isomorphic to \ef^(β) where β is again an ordinal. Finally, the categories of the vector spaces of the the first and the second type are equivalent.

Related

• Any countable topological \mathbb F_p-vector space has a closed discrete basis
• Discrete Vector Fields and Fundamental Algebraic Topology
• Free modules with isomorphic duals
• L vector spaces and L fields
• Notes on topological vector spaces