Hahn–Banach theorem (English Wikipedia)

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

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See M. Riesz extension theorem. According to Gårding, L. (1970). "Marcel Riesz in memoriam". Acta Math. 124 (1): I–XI. doi:10.1007/bf02394565. MR 0256837., the argument was known to Riesz already in 1918.
Zălinescu, C. (2002). Convex analysis in general vector spaces. River Edge, NJ: World Scientific Publishing Co., Inc. pp. 5–7. ISBN 981-238-067-1. MR 1921556.
Simpson, Stephen G. (2009), Subsystems of second order arithmetic, Perspectives in Logic (2nd ed.), Cambridge University Press, ISBN 978-0-521-88439-6, MR2517689

archive.org

Rudin 1991, pp. 56–62. 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.
Rudin 1991, Th. 3.2 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.
Rudin 1991, Th. 3.2 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.
Rudin 1991, p. 141. 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.

doi.org

See M. Riesz extension theorem. According to Gårding, L. (1970). "Marcel Riesz in memoriam". Acta Math. 124 (1): I–XI. doi:10.1007/bf02394565. MR 0256837., the argument was known to Riesz already in 1918.
Luxemburg 1962. Luxemburg, W. A. J. (1962). "Two Applications of the Method of Construction by Ultrapowers to Analysis". Bulletin of the American Mathematical Society. 68 (4). American Mathematical Society: 416–419. doi:10.1090/s0002-9904-1962-10824-6. ISSN 0273-0979.
Łoś & Ryll-Nardzewski 1951, pp. 233–237. Łoś, Jerzy; Ryll-Nardzewski, Czesław (1951). "On the application of Tychonoff's theorem in mathematical proofs". Fundamenta Mathematicae. 38 (1): 233–237. doi:10.4064/fm-38-1-233-237. ISSN 0016-2736. Retrieved 7 July 2022.
Harvey, R.; Lawson, H. B. (1983). "An intrinsic characterisation of Kähler manifolds". Invent. Math. 74 (2): 169–198. Bibcode:1983InMat..74..169H. doi:10.1007/BF01394312. S2CID 124399104.
Kutateladze, Semen (1996). Fundamentals of Functional Analysis. Kluwer Texts in the Mathematical Sciences. Vol. 12. p. 40. doi:10.1007/978-94-015-8755-6. ISBN 978-90-481-4661-1.
Pincus 1974, pp. 203–205. 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.
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 26 Dec 2021.
Foreman, M.; Wehrung, F. (1991). "The Hahn–Banach theorem implies the existence of a non-Lebesgue measurable set" (PDF). Fundamenta Mathematicae. 138: 13–19. doi:10.4064/fm-138-1-13-19.
Pawlikowski, Janusz (1991). "The Hahn–Banach theorem implies the Banach–Tarski paradox". Fundamenta Mathematicae. 138: 21–22. doi:10.4064/fm-138-1-21-22.
Brown, D. K.; Simpson, S. G. (1986). "Which set existence axioms are needed to prove the separable Hahn–Banach theorem?". Annals of Pure and Applied Logic. 31: 123–144. doi:10.1016/0168-0072(86)90066-7. Source of citation.

eudml.org

Łoś & Ryll-Nardzewski 1951, pp. 233–237. Łoś, Jerzy; Ryll-Nardzewski, Czesław (1951). "On the application of Tychonoff's theorem in mathematical proofs". Fundamenta Mathematicae. 38 (1): 233–237. doi:10.4064/fm-38-1-233-237. ISSN 0016-2736. Retrieved 7 July 2022.

harvard.edu

ui.adsabs.harvard.edu

Harvey, R.; Lawson, H. B. (1983). "An intrinsic characterisation of Kähler manifolds". Invent. Math. 74 (2): 169–198. Bibcode:1983InMat..74..169H. doi:10.1007/BF01394312. S2CID 124399104.

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 26 Dec 2021.
Foreman, M.; Wehrung, F. (1991). "The Hahn–Banach theorem implies the existence of a non-Lebesgue measurable set" (PDF). Fundamenta Mathematicae. 138: 13–19. doi:10.4064/fm-138-1-13-19.

ksu.edu

math.ksu.edu

Gabriel Nagy, Real Analysis lecture notes

projecteuclid.org

Luxemburg 1962. Luxemburg, W. A. J. (1962). "Two Applications of the Method of Construction by Ultrapowers to Analysis". Bulletin of the American Mathematical Society. 68 (4). American Mathematical Society: 416–419. doi:10.1090/s0002-9904-1962-10824-6. ISSN 0273-0979.

psu.edu

math.psu.edu

Brown, D. K.; Simpson, S. G. (1986). "Which set existence axioms are needed to prove the separable Hahn–Banach theorem?". Annals of Pure and Applied Logic. 31: 123–144. doi:10.1016/0168-0072(86)90066-7. Source of citation.

researchgate.net

Kutateladze, Semen (1996). Fundamentals of Functional Analysis. Kluwer Texts in the Mathematical Sciences. Vol. 12. p. 40. doi:10.1007/978-94-015-8755-6. ISBN 978-90-481-4661-1.

semanticscholar.org

api.semanticscholar.org

Harvey, R.; Lawson, H. B. (1983). "An intrinsic characterisation of Kähler manifolds". Invent. Math. 74 (2): 169–198. Bibcode:1983InMat..74..169H. doi:10.1007/BF01394312. S2CID 124399104.

st-andrews.ac.uk

mathshistory.st-andrews.ac.uk

O'Connor, John J.; Robertson, Edmund F., "Hahn–Banach theorem", MacTutor History of Mathematics Archive, University of St Andrews

uwb.edu.pl

mizar.uwb.edu.pl

HAHNBAN file

worldcat.org

search.worldcat.org

Narici & Beckenstein 2011, pp. 177–220. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Rudin 1991, pp. 56–62. 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.
Rudin 1991, Th. 3.2 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. 177–183. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Schechter 1996, pp. 318–319. Schechter, Eric (1996). Handbook of Analysis and Its Foundations. San Diego, CA: Academic Press. ISBN 978-0-12-622760-4. OCLC 175294365.
Rudin 1991, Th. 3.2 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. 126–128. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Luxemburg 1962. Luxemburg, W. A. J. (1962). "Two Applications of the Method of Construction by Ultrapowers to Analysis". Bulletin of the American Mathematical Society. 68 (4). American Mathematical Society: 416–419. doi:10.1090/s0002-9904-1962-10824-6. ISSN 0273-0979.
Łoś & Ryll-Nardzewski 1951, pp. 233–237. Łoś, Jerzy; Ryll-Nardzewski, Czesław (1951). "On the application of Tychonoff's theorem in mathematical proofs". Fundamenta Mathematicae. 38 (1): 233–237. doi:10.4064/fm-38-1-233-237. ISSN 0016-2736. Retrieved 7 July 2022.
Narici & Beckenstein 2011, pp. 182, 498. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Narici & Beckenstein 2011, p. 184. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Narici & Beckenstein 2011, p. 182. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Narici & Beckenstein 2011, p. 126. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Trèves 2006, p. 184. Trèves, François (2006) [1967]. Topological Vector Spaces, Distributions and Kernels. Mineola, N.Y.: Dover Publications. ISBN 978-0-486-45352-1. OCLC 853623322.
Narici & Beckenstein 2011, pp. 195. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Schaefer & Wolff 1999, p. 47. Schaefer, Helmut H.; Wolff, Manfred P. (1999). Topological Vector Spaces. GTM. Vol. 8 (Second ed.). New York, NY: Springer New York Imprint Springer. ISBN 978-1-4612-7155-0. OCLC 840278135.
Narici & Beckenstein 2011, p. 212. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Wilansky 2013, pp. 18–21. Wilansky, Albert (2013). Modern Methods in Topological Vector Spaces. Mineola, New York: Dover Publications, Inc. ISBN 978-0-486-49353-4. OCLC 849801114.
Narici & Beckenstein 2011, pp. 150. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Rudin 1991, p. 141. 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.
Edwards 1995, pp. 124–125. Edwards, Robert E. (1995). Functional Analysis: Theory and Applications. New York: Dover Publications. ISBN 978-0-486-68143-6. OCLC 30593138.
Narici & Beckenstein 2011, pp. 225–273. Narici, Lawrence; Beckenstein, Edward (2011). Topological Vector Spaces. Pure and applied mathematics (Second ed.). Boca Raton, FL: CRC Press. ISBN 978-1584888666. OCLC 144216834.
Pincus 1974, pp. 203–205. 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.
Schechter 1996, pp. 766–767. Schechter, Eric (1996). Handbook of Analysis and Its Foundations. San Diego, CA: Academic Press. ISBN 978-0-12-622760-4. OCLC 175294365.