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A Serre‐Swan Theorem for Bundles of Topological Modules
Author(s) -
Papatriantafillou Maria H.
Publication year - 1992
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19921560119
Subject(s) - mathematics , pure mathematics , hausdorff space , invertible matrix , finitely generated abelian group , type (biology) , topology (electrical circuits) , discrete mathematics , combinatorics , ecology , biology
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 .