Extension of invariant linear functionals: Hahn-Banach in the topos of M- sets

DOI10.1016/0022-4049(80)90047-XzbMath0453.18003OpenAlexW2075513489MaRDI QIDQ1148983

Bernhard Banaschewski

Publication date: 1980

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(80)90047-x

zbMATH Keywords

Hahn-Banach theoremBoolean prime ideal theoremultrafilter theoremtopological monoidBanach sheafinjectivity for Banach objectstopos of M-sets

Mathematics Subject Classification ID

Normed linear spaces and Banach spaces; Banach lattices (46B99) Analysis on topological semigroups (22A20) Projective and injective objects in functional analysis (46M10) Topoi (18B25) Representation of semigroups; actions of semigroups on sets (20M30)

Related Items (9)

The point of pointless topology ⋮ Injectivity and modelling in the Blass topos ⋮ The Gleason cover of a topos. I ⋮ A globalization of the Hahn-Banach theorem ⋮ Theory of topological molecular lattices ⋮ \(z\)-ideals in the real continuous function ring \(\mathcal{R}(L_{\tau}) \) ⋮ Abelian groups in a topos: injectives and injective effacements ⋮ A globalisation of the Gelfand duality theorem ⋮ Locales in functional analysis

Cites Work

• The Hahn-Banach theorem in a category of sheaves
• Banach sheaves
• On Invariant Means Over Compact Semigroups
• Two applications of the method of construction by ultrapowers to analysis
• SHEAVES OF BANACH SPEACES
• Some Remarks on Injective Envelopes
• Independence of the prime ideal theorem from the Hahn Banach theorem
• Injective envelopes of Banach spaces
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