Klee, Victor L. jun. Convex bodies and periodic homeomorphisms in Hilbert space. (English) Zbl 0050.33202 Trans. Am. Math. Soc. 74, 10-43 (1953). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 72 Documents Keywords:functional analysis PDF BibTeX XML Cite \textit{V. L. Klee jun.}, Trans. Am. Math. Soc. 74, 10--43 (1953; Zbl 0050.33202) Full Text: DOI OpenURL References: [1] Stefan Banach, Théorie des opérations linéaires, Warsaw, 1932. · Zbl 0005.20901 [2] S. Banach and S. Mazur, Zur Theorie der linearen Dimension, Studia Math. vol. 4 (1933) pp. 100-112. · JFM 59.1075.01 [3] William A. Blankinship, Generalization of a construction of Antoine, Ann. of Math. (2) 53 (1951), 276 – 297. · Zbl 0042.17601 [4] K. Borsuk, Über Isomorphie der Funktionalraume, Bulletin International de l’Académie Polonaise des Sciences et des Lettres Ser. A (1933) pp. 1-10. [5] Herbert Busemann, Note on a theorem on convex sets, Mat. Tidsskr. B. 1947 (1947), 32 – 34. · Zbl 0040.38403 [6] James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396 – 414. · Zbl 0015.35604 [7] J. Dugundji, An extension of Tietze’s theorem, Pacific J. Math. 1 (1951), 353 – 367. · Zbl 0043.38105 [8] W. F. Eberlein, Weak compactness in Banach spaces. I, Proc. Nat. Acad. Sci. U. S. A. 33 (1947), 51 – 53. · Zbl 0029.26902 [9] Samuel Eilenberg, On the problems of topology, Ann. of Math. (2) 50 (1949), 247 – 260. · Zbl 0034.25304 [10] Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. · Zbl 0060.39808 [11] Børge Jessen, Two theorems on convex point sets, Mat. Tidsskr. B. 1940 (1940), 66-70 (Danish). [12] S. Kaczmarz, The homeomorphy of certain spaces, Bulletin International de l’Académie Polonaise des Sciences et des Lettres Ser. A (1933) pp. 145-148. · Zbl 0008.16503 [13] Shizuo Kakutani, Topological properties of the unit sphere of a Hilbert space, Proc. Imp. Acad. Tokyo 19 (1943), 269 – 271. · Zbl 0060.27701 [14] Ott-Heinrich Keller, Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. 105 (1931), no. 1, 748 – 758 (German). · Zbl 0003.22401 [15] V. L. Klee Jr., Convex sets in linear spaces, Duke Math. J. 18 (1951), 443 – 466. · Zbl 0042.36201 [16] V. L. Klee Jr., Convex sets in linear spaces. II, Duke Math. J. 18 (1951), 875 – 883. · Zbl 0044.11201 [17] V. L. Klee Jr., Invariant metrics in groups (solution of a problem of Banach), Proc. Amer. Math. Soc. 3 (1952), 484 – 487. · Zbl 0047.02902 [18] 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). · Zbl 0023.13105 [19] M. Krein and V. Šmulian, On regulary convex sets in the space conjugate to a Banach space, Ann. of Math. (2) 41 (1940), 556 – 583. · JFM 66.0533.02 [20] 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. · Zbl 0015.08204 [21] Solomon Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications, v. 27, American Mathematical Society, New York, 1942. · Zbl 0061.39302 [22] S. Mazur, Une remarque sur l’homeomorphie des champs fonctionnels, Studia Math. vol. 1 (1929) pp. 83-85. · JFM 55.0242.01 [23] -, Über die kleinsten konvexe Mengen, die eine gegebene kompakte Menge enthalt, Studia Math. vol. 2 (1930) pp. 7-9. · JFM 56.0091.01 [24] Edward James McShane, Integration, Princeton University Press, Princeton, N. J., 1944 1957. · Zbl 0060.13010 [25] Deane Montgomery, Pointwise Periodic Homeomorphisms, Amer. J. Math. 59 (1937), no. 1, 118 – 120. · Zbl 0016.08201 [26] P.A. Smith, Fixed-point theorems for periodic transformations, Amer. J. Math. 63 (1941), 1 – 8. · Zbl 0024.19004 [27] P. A. Smith, Transformations of finite period. III. Newman’s theorem, Ann. of Math. (2) 42 (1941), 446 – 458. · JFM 67.0743.01 [28] V. Šmulian, On the principle of inclusion in the space of the type (\?), Rec. Math. [Mat. Sbornik] N.S. 5(47) (1939), 317 – 328 (Russian, with English summary). · JFM 65.1312.02 [29] J. J. Stoker, Unbounded convex point sets, Amer. J. Math. 62 (1940), 165 – 179. · Zbl 0022.40301 [30] M. H. Stone, Note on integration. II, Proc. Nat. Acad. Sci. U. S. A. 34 (1948), 447 – 455. · Zbl 0034.02903 [31] A. Tychonoff, Ein Fixpunktsatz, Math. Ann. 111 (1935), no. 1, 767 – 776 (German). · Zbl 0012.30803 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.