2024/06/17 by Alexandru Chirvăsitu, Chirvasitu, Alexandru
Mathematics · Medicine · #13C10 #13C11 #18A30 #18D15 #18D20 #18M05 #46E25 #46H25 #46J10 #46M20 #Advanced Topics in Algebra #Category Theory (math.CT) #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN) #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications #Operator Algebras (math.OA) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2406.11221
openalex publication_date 2024/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We show that a continuously-normed Banach bundle E over a compact Hausdorff space X whose space of sections is algebraically finitely-generated (f.g.) over C(X) is locally trivial (and hence the section space is projective f.g over C(X)); this answers a question of I. Gogić. As a preliminary we also provide sufficient conditions for a quotient bundle to be continuous phrased in terms of the Vietoris continuity of the unit-ball maps attached to the bundles. Related results include (a) the fact that the category of topologically f.g. continuous Banach bundles over X is symmetric monoidal under the (fiber-wise-maximal) tensor product, (b) the full faithfulness of the global-section functor from topologically f.g. continuous bundles to C(X)-modules and (c) the consequent identification of the algebraically f.g. bundles as precisely the rigid objects in the aforementioned symmetric monoidal category.