✦ LIBER ✦
A Serre-Swan Theorem for Bundles of Topological Modules
✍ Scribed by Maria H. Papatriantafillou
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 436 KB
- Volume
- 156
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
Let R be a unital topological ring whose set of invertible elements is open and inversion is continuous, and let X be a compact Hausdorff space admitting continuous R‐valued partitions of unity. Considering bundles over X of fibre type a projective finitely generated R‐module, we prove a Serre‐Swan type theorem: namely, the category of these bundles is equivalent to the category of projective finitely generated modules over the ring of continuous R‐valued functions on X.