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==Bibliography== * {{Adasch Topological Vector Spaces}} <!--{{sfn|Adasch|1978|p=}}--> * {{Banach Théorie des Opérations Linéaires}} <!--{{sfn|Banach|1932|p=}}--> * {{Berberian Lectures in Functional Analysis and Operator Theory}} <!--{{sfn|Berberian|2014|p=}}--> * {{Bourbaki Topological Vector Spaces}} <!--{{sfn|Bourbaki|1987|p=}}--> * {{Conway A Course in Functional Analysis}} <!--{{sfn|Conway|1990|p=}}--> * {{Edwards Functional Analysis Theory and Applications}} <!--{{sfn|Edwards|1995|p=}}--> * {{Grothendieck Topological Vector Spaces}} <!--{{sfn|Grothendieck|1973|p=}}--> * {{Jarchow Locally Convex Spaces}} <!--{{sfn|Jarchow|1981|p=}}--> * {{Köthe Topological Vector Spaces I}} <!--{{sfn|Köthe| 1983|p=}}--> * {{cite journal|last1=Łoś|first1=Jerzy|author-link1=Jerzy Łoś|last2=Ryll-Nardzewski|first2=Czesław|author-link2=Czesław Ryll-Nardzewski|title=On the application of Tychonoff's theorem in mathematical proofs|journal=Fundamenta Mathematicae|volume=38|issue=1|date=1951|issn=0016-2736|pages=233–237|doi=10.4064/fm-38-1-233-237 |url=https://eudml.org/doc/213246|access-date=7 July 2022|doi-access=free}} <!--{{sfn|Łoś|Ryll-Nardzewski|1951|pp=233–237}}--> * {{cite journal|last=Luxemburg|first=W. A. J.|author-link=Wilhelmus Luxemburg|title=Two Applications of the Method of Construction by Ultrapowers to Analysis|url=https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society-new-series/volume-68/issue-4/Two-applications-of-the-method-of-construction-by-ultrapowers-to/bams/1183524688.full|journal=[[Bulletin of the American Mathematical Society]]|publisher=American Mathematical Society|volume=68|issue=4|year=1962|issn=0273-0979|pages=416–419|doi=10.1090/s0002-9904-1962-10824-6|doi-access=free}} <!--{{sfn|Luxemburg|1962|p=}}--> * {{cite book|last=Narici|first=Lawrence|title=Advanced Courses of Mathematical Analysis II|chapter=On the Hahn-Banach Theorem|year=2007|publisher=World Scientific|pages=87–122|doi=10.1142/9789812708441_0006|isbn=978-981-256-652-2 |doi-access=|url=http://at.yorku.ca/p/a/a/o/58.pdf|access-date=7 July 2022}} <!--{{sfn|Narici|2007|p=}}--> * {{cite journal|last1=Narici|first1=Lawrence|last2=Beckenstein|first2=Edward|year=1997|title=The Hahn–Banach Theorem: The Life and Times|url=http://at.yorku.ca/p/a/a/a/16.htm|journal=Topology and Its Applications|volume=77|issue=2|pages=193–211|doi=10.1016/s0166-8641(96)00142-3|doi-access=}} <!--{{sfn|Narici|Beckenstein|1997|p=}}--> * {{Narici Beckenstein Topological Vector Spaces|edition=2}} <!--{{sfn|Narici|Beckenstein|2011|p=}}--> * {{cite journal|last=Pincus|first=David|author-link=David Pincus|title=Independence of the prime ideal theorem from the Hahn Banach theorem|journal=Bulletin of the American Mathematical Society|publisher=American Mathematical Society|volume=78|issue=5|year=1972|issn=0273-0979|doi=10.1090/s0002-9904-1972-13025-8|pages=766–770|url=https://www.ams.org/journals/bull/1972-78-05/S0002-9904-1972-13025-8/S0002-9904-1972-13025-8.pdf|access-date=7 July 2022}} <!--{{sfn|Pincus|1972|pp=766–770}}--> * {{cite book|last=Pincus|first=David|author-link=David Pincus|editor-last1=Hurd|editor-first1=A.|editor-last2=Loeb|editor-first2=P.|year=1974|title=Victoria Symposium on Nonstandard Analysis|chapter=The strength of the Hahn-Banach theorem|series=Lecture Notes in Mathematics|pages=203–248|volume=369|publisher=Springer|publication-place=Berlin, Heidelberg|isbn=978-3-540-06656-9|issn=0075-8434|doi=10.1007/bfb0066014}} <!--{{sfn|Pincus|1974|p=}}--> * Reed, Michael and Simon, Barry, ''Methods of Modern Mathematical Physics, Vol. 1, Functional Analysis,'' Section III.3. Academic Press, San Diego, 1980. {{ISBN|0-12-585050-6}}. * {{Cite book|last1=Reed|first1=Michael|author-link1=Michael C. Reed|last2=Simon|first2=Barry|author2-link=Barry Simon|title=Functional Analysis|publisher=[[Academic Press]]|location=Boston, MA|edition=revised and enlarged|isbn=978-0-12-585050-6|year=1980}} * {{Robertson Topological Vector Spaces}} <!--{{sfn|Robertson|1964|p=}}--> * {{Rudin Walter Functional Analysis|edition=2}} <!--{{sfn|Rudin|1991|p=}}--> * {{Schaefer Wolff Topological Vector Spaces|edition=2}} <!--{{sfn|Schaefer|Wolff|1999|p=}}--> * {{cite journal|last1=Schmitt|first1=Lothar M|year=1992|title=An Equivariant Version of the Hahn–Banach Theorem|url=http://www.math.uh.edu/~hjm/vol18-3.html|journal=Houston J. Of Math.|volume=18|pages=429–447}} * {{Schechter Handbook of Analysis and Its Foundations}}<!--{{ISBN|0-12-622760-8}}--> <!--{{sfn|Schechter|1996|p=}}--> * {{Swartz An Introduction to Functional Analysis}} <!--{{sfn|Swartz|1992|p=}}--> * [[Terence Tao|Tao, Terence]], [http://terrytao.wordpress.com/2007/11/30/the-hahn-banach-theorem-mengers-theorem-and-hellys-theorem The Hahn–Banach theorem, Menger's theorem, and Helly's theorem] * {{Trèves François Topological vector spaces, distributions and kernels}} <!--{{sfn|Trèves|2006|p=}}--> * {{Wilansky Modern Methods in Topological Vector Spaces}} <!--{{sfn|Wilansky|2013|p=}}--> * Wittstock, Gerd, Ein operatorwertiger Hahn-Banach Satz, [http://www.sciencedirect.com/science/article/pii/0022123681900641 J. of Functional Analysis 40 (1981), 127–150] * Zeidler, Eberhard, ''Applied Functional Analysis: main principles and their applications'', Springer, 1995. * {{springer|title=Hahn–Banach theorem|id=p/h046130}} {{Functional Analysis}} {{TopologicalVectorSpaces}} {{Banach spaces}} {{DEFAULTSORT:Hahn-Banach theorem}} [[Category:Articles containing proofs]] [[Category:Linear algebra]] [[Category:Linear functionals]] [[Category:Theorems in functional analysis]] [[Category:Topological vector spaces]]
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