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Abstract: Using the notion of entailment relation [Sco74] we give a direct proof of the localic version of Hahn-Banach's theorem. 1 Introduction There are several examples of topological spaces naturally associated to a mathematical structure: the spectrum (with Zariski topology) associated to a ring, the space of valuations associated to a field, and the space Fn E of linear functionals of norm not exceding 1 associated to a normed vector space E. In most of these examples, the associated space is... (Update)
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BibTeX entry: (Update)
@misc{ coquand-direct,
author = "Thierry Coquand",
title = "A Direct Proof of the Localic Hahn-Banach Theorem",
url = "citeseer.ist.psu.edu/coquand99direct.html" }
Citations (may not include all citations):126 Cambridge University Press (context) - Johnstone - 1982
13 A globalization of the hahn-banach theorem (context) - Mulvey, Pelletier - 1991
5 Valuation ring and dedekind prague's theorem (context) - Coquand, Persson - 1998
4 Completeness and axiomatiszability (context) - Scott - 1974
4 Constructive techniques in functional analysis (context) - Vermeulen - 1986
3 Dimension of boolean valued lattices and rings (context) - Espanol - 1986
2 to appear in 25 years in Constructive Type Theory (context) - Cederquist, Coquand et al. - 1998
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Valuations and Dedekind's Prague Theorem - Coquand, Persson (Correct)
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