Convex bodies and periodic homeomorphisms in Hilbert space
HTML articles powered by AMS MathViewer
- by Victor L. Klee
- Trans. Amer. Math. Soc. 74 (1953), 10-43
- DOI: https://doi.org/10.1090/S0002-9947-1953-0054850-X
- PDF | Request permission
References
- Stefan Banach, Théorie des opérations linéaires, Warsaw, 1932.
S. Banach and S. Mazur, Zur Theorie der linearen Dimension, Studia Math. vol. 4 (1933) pp. 100-112.
- William A. Blankinship, Generalization of a construction of Antoine, Ann. of Math. (2) 53 (1951), 276–297. MR 40659, DOI 10.2307/1969543 K. Borsuk, Über Isomorphie der Funktionalraume, Bulletin International de l’Académie Polonaise des Sciences et des Lettres Ser. A (1933) pp. 1-10.
- Herbert Busemann, Note on a theorem on convex sets, Mat. Tidsskr. B 1947 (1947), 32–34. MR 23087
- James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396–414. MR 1501880, DOI 10.1090/S0002-9947-1936-1501880-4
- J. Dugundji, An extension of Tietze’s theorem, Pacific J. Math. 1 (1951), 353–367. MR 44116
- W. F. Eberlein, Weak compactness in Banach spaces. I, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 51–53. MR 21239, DOI 10.1073/pnas.33.3.51
- Samuel Eilenberg, On the problems of topology, Ann. of Math. (2) 50 (1949), 247–260. MR 30189, DOI 10.2307/1969448
- Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, vol. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
- Børge Jessen, Two theorems on convex point sets, Mat. Tidsskr. B 1940 (1940), 66–70 (Danish). MR 3721 S. Kaczmarz, The homeomorphy of certain spaces, Bulletin International de l’Académie Polonaise des Sciences et des Lettres Ser. A (1933) pp. 145-148.
- Shizuo Kakutani, Topological properties of the unit sphere of a Hilbert space, Proc. Imp. Acad. Tokyo 19 (1943), 269–271. MR 14203
- Ott-Heinrich Keller, Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. 105 (1931), no. 1, 748–758 (German). MR 1512740, DOI 10.1007/BF01455844
- V. L. Klee Jr., Convex sets in linear spaces, Duke Math. J. 18 (1951), 443–466. MR 44014
- V. L. Klee Jr., Convex sets in linear spaces. II, Duke Math. J. 18 (1951), 875–883. MR 47251
- V. L. Klee Jr., Invariant metrics in groups (solution of a problem of Banach), Proc. Amer. Math. Soc. 3 (1952), 484–487. MR 47250, DOI 10.1090/S0002-9939-1952-0047250-4
- M. Krein, D. Milman, and M. Rutman, A note on basis in Banach space, Comm. Inst. Sci. Math. Méc. Univ. Kharkoff [Zapiski Inst. Mat. Mech.] (4) 16 (1940), 106–110 (Russian, with English summary). MR 0004709
- M. Krein and V. Šmulian, On regularly convex sets in the space conjugate to a Banach space, Ann. of Math. (2) 41 (1940), 556–583. MR 2009, DOI 10.2307/1968735 Kazimierz Kuratowski, Une condition metrique pour la retraction des ensembles, Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie vol. 28 (1936) pp. 156-158.
- Solomon Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications, Vol. 27, American Mathematical Society, New York, 1942. MR 0007093 S. Mazur, Une remarque sur l’homeomorphie des champs fonctionnels, Studia Math. vol. 1 (1929) pp. 83-85. —, Über die kleinsten konvexe Mengen, die eine gegebene kompakte Menge enthalt, Studia Math. vol. 2 (1930) pp. 7-9.
- Edward James McShane, Integration, Princeton University Press, Princeton, N. J., 1944 1957. MR 0082536
- Deane Montgomery, Pointwise Periodic Homeomorphisms, Amer. J. Math. 59 (1937), no. 1, 118–120. MR 1507223, DOI 10.2307/2371565
- P.A. Smith, Fixed-point theorems for periodic transformations, Amer. J. Math. 63 (1941), 1–8. MR 3199, DOI 10.2307/2371271
- P. A. Smith, Transformations of finite period. III. Newman’s theorem, Ann. of Math. (2) 42 (1941), 446–458. MR 4128, DOI 10.2307/1968910
- V. Šmulian, On the principle of inclusion in the space of the type $(\textrm {B})$, Rec. Math. [Mat. Sbornik] N.S. 5(47) (1939), 317–328 (Russian, with English summary). MR 0002006
- J. J. Stoker, Unbounded convex point sets, Amer. J. Math. 62 (1940), 165–179. MR 1029, DOI 10.2307/2371445
- M. H. Stone, Note on integration. II, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 447–455. MR 26102, DOI 10.1073/pnas.34.9.447
- A. Tychonoff, Ein Fixpunktsatz, Math. Ann. 111 (1935), no. 1, 767–776 (German). MR 1513031, DOI 10.1007/BF01472256
Bibliographic Information
- © Copyright 1953 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 74 (1953), 10-43
- MSC: Primary 46.0X
- DOI: https://doi.org/10.1090/S0002-9947-1953-0054850-X
- MathSciNet review: 0054850