Krein–Milman theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Krein–Milman theorem" in English language version.

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Rudin 1991, p. 75 Theorem 3.23. Rudin, Walter (1991). Functional Analysis. International Series in Pure and Applied Mathematics. Vol. 8 (Second ed.). New York, NY: McGraw-Hill Science/Engineering/Math. ISBN 978-0-07-054236-5. OCLC 21163277.
Grothendieck 1973, pp. 187–188. Grothendieck, Alexander (1973). Topological Vector Spaces. Translated by Chaljub, Orlando. New York: Gordon and Breach Science Publishers. ISBN 978-0-677-30020-7. OCLC 886098.

arxiv.org

Monod, Nicolas (2016), "Extreme points in non-positive curvature", Studia Mathematica, 234: 265–270, arXiv:1602.06752
Buehler, Theo (2006), The Krein–Mil'man theorem for metric spaces with a convex bicombing, arXiv:math/0604187, Bibcode:2006math......4187B

books.google.com

Aliprantis & Border 2006, p. 185. Aliprantis, Charalambos D.; Border, Kim C. (2006). Infinite Dimensional Analysis: A Hitchhiker's Guide (Third ed.). Berlin: Springer Science & Business Media. ISBN 978-3-540-29587-7. OCLC 262692874.

doi.org

Pincus 1974, pp. 204–205. Pincus, David (1974). "The strength of the Hahn-Banach theorem". In Hurd, A.; Loeb, P. (eds.). Victoria Symposium on Nonstandard Analysis. Lecture Notes in Mathematics. Vol. 369. Berlin, Heidelberg: Springer. pp. 203–248. doi:10.1007/bfb0066014. ISBN 978-3-540-06656-9. ISSN 0075-8434.
Roberts, J. (1977), "A compact convex set with no extreme points", Studia Mathematica, 60 (3): 255–266, doi:10.4064/sm-60-3-255-266
Bell, J.; Fremlin, David (1972). "A geometric form of the axiom of choice" (PDF). Fundamenta Mathematicae. 77 (2): 167–170. doi:10.4064/fm-77-2-167-170. Retrieved 11 June 2018. Theorem 1.2. BPI [the Boolean Prime Ideal Theorem] & KM [Krein-Milman] $\implies$ (*) [the unit ball of the dual of a normed vector space has an extreme point].... Theorem 2.1. (*) $\implies$ AC [the Axiom of Choice].
Krein, Mark; Milman, David (1940), "On extreme points of regular convex sets", Studia Mathematica, 9: 133–138, doi:10.4064/sm-9-1-133-138
Steinitz, Ernst (1916), "Bedingt konvergente Reihen und konvexe Systeme VI, VII", J. Reine Angew. Math., 146: 1–52, doi:10.1515/crll.1916.146.1, S2CID 122897233; (see p. 16)

eudml.org

Roberts, J. (1977), "A compact convex set with no extreme points", Studia Mathematica, 60 (3): 255–266, doi:10.4064/sm-60-3-255-266
Krein, Mark; Milman, David (1940), "On extreme points of regular convex sets", Studia Mathematica, 9: 133–138, doi:10.4064/sm-9-1-133-138

harvard.edu

ui.adsabs.harvard.edu

Buehler, Theo (2006), The Krein–Mil'man theorem for metric spaces with a convex bicombing, arXiv:math/0604187, Bibcode:2006math......4187B

icm.edu.pl

matwbn.icm.edu.pl

Bell, J.; Fremlin, David (1972). "A geometric form of the axiom of choice" (PDF). Fundamenta Mathematicae. 77 (2): 167–170. doi:10.4064/fm-77-2-167-170. Retrieved 11 June 2018. Theorem 1.2. BPI [the Boolean Prime Ideal Theorem] & KM [Krein-Milman] $\implies$ (*) [the unit ball of the dual of a normed vector space has an extreme point].... Theorem 2.1. (*) $\implies$ AC [the Axiom of Choice].

semanticscholar.org

api.semanticscholar.org

Steinitz, Ernst (1916), "Bedingt konvergente Reihen und konvexe Systeme VI, VII", J. Reine Angew. Math., 146: 1–52, doi:10.1515/crll.1916.146.1, S2CID 122897233; (see p. 16)

uwo.ca

publish.uwo.ca

Bell, J. L.; Jellett, F. (1971). "On the Relationship Between the Boolean Prime Ideal Theorem and Two Principles in Functional Analysis" (PDF). Bull. Acad. Polon. Sci. sciences math., astr. et phys. 19 (3): 191–194. Retrieved 23 Dec 2021.

worldcat.org

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Rudin 1991, p. 75 Theorem 3.23. Rudin, Walter (1991). Functional Analysis. International Series in Pure and Applied Mathematics. Vol. 8 (Second ed.). New York, NY: McGraw-Hill Science/Engineering/Math. ISBN 978-0-07-054236-5. OCLC 21163277.
Narici & Beckenstein 2011, pp. 275–339. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Aliprantis & Border 2006, p. 185. Aliprantis, Charalambos D.; Border, Kim C. (2006). Infinite Dimensional Analysis: A Hitchhiker's Guide (Third ed.). Berlin: Springer Science & Business Media. ISBN 978-3-540-29587-7. OCLC 262692874.
Trèves 2006, p. 145. Trèves, François (2006) [1967]. Topological Vector Spaces, Distributions and Kernels. Mineola, N.Y.: Dover Publications. ISBN 978-0-486-45352-1. OCLC 853623322.
Trèves 2006, p. 67. Trèves, François (2006) [1967]. Topological Vector Spaces, Distributions and Kernels. Mineola, N.Y.: Dover Publications. ISBN 978-0-486-45352-1. OCLC 853623322.
Grothendieck 1973, pp. 187–188. Grothendieck, Alexander (1973). Topological Vector Spaces. Translated by Chaljub, Orlando. New York: Gordon and Breach Science Publishers. ISBN 978-0-677-30020-7. OCLC 886098.
Pincus 1974, pp. 204–205. Pincus, David (1974). "The strength of the Hahn-Banach theorem". In Hurd, A.; Loeb, P. (eds.). Victoria Symposium on Nonstandard Analysis. Lecture Notes in Mathematics. Vol. 369. Berlin, Heidelberg: Springer. pp. 203–248. doi:10.1007/bfb0066014. ISBN 978-3-540-06656-9. ISSN 0075-8434.