• [1] Stefan Banach, Théorie des opérations linéaires, Warsaw, 1932.
• [2] S. Banach and S. Mazur, Zur Theorie der linearen Dimension, Studia Math. vol. 4 (1933) pp. 100-112.
• [3] William A. Blankinship, Generalization of a construction of Antoine, Ann. of Math. (2) 53 (1951), 276–297. MR 40659, https://doi.org/10.2307/1969543
• [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. MR 23087
• [6] James A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396–414. MR 1501880, https://doi.org/10.1090/S0002-9947-1936-1501880-4
• [7] J. Dugundji, An extension of Tietze’s theorem, Pacific J. Math. 1 (1951), 353–367. MR 44116
• [8] W. F. Eberlein, Weak compactness in Banach spaces. I, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 51–53. MR 21239, https://doi.org/10.1073/pnas.33.3.51
• [9] Samuel Eilenberg, On the problems of topology, Ann. of Math. (2) 50 (1949), 247–260. MR 30189, https://doi.org/10.2307/1969448
• [10] Witold Hurewicz and Henry Wallman, Dimension Theory, Princeton Mathematical Series, v. 4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
• [11] Børge Jessen, Two theorems on convex point sets, Mat. Tidsskr. B 1940 (1940), 66-70 (Danish). MR 3721
• [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.
• [13] Shizuo Kakutani, Topological properties of the unit sphere of a Hilbert space, Proc. Imp. Acad. Tokyo 19 (1943), 269–271. MR 14203
• [14] Ott-Heinrich Keller, Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. 105 (1931), no. 1, 748–758 (German). MR 1512740, https://doi.org/10.1007/BF01455844
• [15] V. L. Klee Jr., Convex sets in linear spaces, Duke Math. J. 18 (1951), 443–466. MR 44014
• [16] V. L. Klee Jr., Convex sets in linear spaces. II, Duke Math. J. 18 (1951), 875–883. MR 47251
• [17] V. L. Klee Jr., Invariant metrics in groups (solution of a problem of Banach), Proc. Amer. Math. Soc. 3 (1952), 484–487. MR 47250, https://doi.org/10.1090/S0002-9939-1952-0047250-4
• [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). MR 0004709
• [19] 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, https://doi.org/10.2307/1968735
• [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.
• [21] Solomon Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications, v. 27, American Mathematical Society, New York, 1942. MR 0007093
• [22] S. Mazur, Une remarque sur l'homeomorphie des champs fonctionnels, Studia Math. vol. 1 (1929) pp. 83-85.
• [23] -, Über die kleinsten konvexe Mengen, die eine gegebene kompakte Menge enthalt, Studia Math. vol. 2 (1930) pp. 7-9.
• [24] Edward James McShane, Integration, Princeton University Press, Princeton, N. J., 1944 1957. MR 0082536
• [25] Deane Montgomery, Pointwise Periodic Homeomorphisms, Amer. J. Math. 59 (1937), no. 1, 118–120. MR 1507223, https://doi.org/10.2307/2371565
• [26] P.A. Smith, Fixed-point theorems for periodic transformations, Amer. J. Math. 63 (1941), 1–8. MR 3199, https://doi.org/10.2307/2371271
• [27] P. A. Smith, Transformations of finite period. III. Newman’s theorem, Ann. of Math. (2) 42 (1941), 446–458. MR 4128, https://doi.org/10.2307/1968910
• [28] V. Šmulian, On the principle of inclusion in the space of the type (𝐵), Rec. Math. [Mat. Sbornik] N.S. 5(47) (1939), 317–328 (Russian, with English summary). MR 0002006
• [29] J. J. Stoker, Unbounded convex point sets, Amer. J. Math. 62 (1940), 165–179. MR 1029, https://doi.org/10.2307/2371445
• [30] M. H. Stone, Note on integration. II, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 447–455. MR 26102, https://doi.org/10.1073/pnas.34.9.447
• [31] A. Tychonoff, Ein Fixpunktsatz, Math. Ann. 111 (1935), no. 1, 767–776 (German). MR 1513031, https://doi.org/10.1007/BF01472256

Bibliography

[1]

Stefan Banach, Théorie des opérations linéaires, Warsaw, 1932.

[2]

S. Banach and S. Mazur, Zur Theorie der linearen Dimension, Studia Math. vol. 4 (1933) pp. 100-112.

[3]

W. A. Blankinship, Generalization of a construction by Antoine, Ann. of Math. vol. 53 (1951) pp. 276-297. MR 0040659 (12:730c)

[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]

H. Busemann, Note on a theorem on convex sets, Matematisk Tidsskrift (1947) pp. 32-34. MR 0023087 (9:302c)

[6]

J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. vol. 40 (1936) pp. 396-414. MR 1501880

[7]

J. Dugundji, An extension of Tietze's theorem, Pacific Journal of Mathematics vol. 1 (1951) pp. 353-367. MR 0044116 (13:373c)

[8]

W. F. Eberlein, Weak compactness in Banach spaces, I, Proc. Nat. Acad. Sci. U. S. A. vol. 33 (1947) pp. 51-53. MR 0021239 (9:42a)

[9]

Samuel Eilenberg, On the problems of topology, Ann. of Math. vol. 50 (1949) pp. 247-260. MR 0030189 (10:726b)

[10]

Witold Hurewicz and Henry Wallman, Dimension theory, Princeton, 1941. MR 0006493 (3:312b)

[11]

B. Jessen, Two theorems on convex points sets (Danish), Matematisk Tidsskrift (1940) pp. 66-70. MR 0003721 (2:261a)

[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.

[13]

Shizuo Kakutani, Topological properties of the unit sphere of a Hilbert space, Proc. Imp. Acad. Tokyo vol. 19 (1943) pp. 269-271. MR 0014203 (7:252l)

[14]

Ott-Heinrich Keller, Die Homoiomorphie der kompakten konvexen Mengen im Hilbertschen Raum, Math. Ann. vol. 105 (1931) pp. 748-758. MR 1512740

[15]

V. L. Klee, Jr., Convex sets in linear spaces, Duke Math. J. vol. 18 (1951) pp. 443-466. MR 0044014 (13:354f)

[16]

-, Convex sets in linear spaces. II., Duke Math. J. vol. 18 (1951) pp. 875-883. MR 0047251 (13:849a)

[17]

-, Invariant metrics in groups (solution of a problem of Banach), Proceedings of the American Mathematical Society vol. 3 (1952) pp. 484-487. MR 0047250 (13:848g)

[18]

M. Krein, D. Milman, and M. Rutman, A note on basis in Banach space, Communications de l'Institut des Sciences Mathématiques et Mécaniques de l'Université de Kharkoff [et de la Société Mathématique de Kharkoff] (4) vol. 6 (1940) pp. 106-110. MR 0004709 (3:49d)

[19]

M. Krein and V. Šmulian, On regularly convex sets in the space conjugate to a Banach space, Ann. of Math. (2) vol. 41 (1940) pp. 556-583. MR 0002009 (1:335e)

[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.

[21]

Solomon Lefschetz, Algebraic topology, Amer. Math. Soc. Colloquium Publications, vol. 27, New York, 1942. MR 0007093 (4:84f)

[22]

S. Mazur, Une remarque sur l'homeomorphie des champs fonctionnels, Studia Math. vol. 1 (1929) pp. 83-85.

[23]

-, Über die kleinsten konvexe Mengen, die eine gegebene kompakte Menge enthalt, Studia Math. vol. 2 (1930) pp. 7-9.

[24]

Edward James McShane, Integration, Princeton, 1944. MR 0082536 (18:567a)

[25]

D. Montgomery, Pointwise periodic homeomorphisms, Amer. J. Math. vol. 59 (1937) pp. 118-120. MR 1507223

[26]

P. A. Smith, Fixed-point theorems for periodic transformations, Amer. J. Math. vol. 63 (1941) pp. 1-8. MR 0003199 (2:179c)

[27]

-, Transformations of finite period, III. Newman's theorem, Ann. of Math. vol. 42 (1941) pp. 446-458. MR 0004128 (2:324c)

[28]

V. Šmulian, On the principle of inclusion in the space of the type (B), Rec. Math. (Mat. Sbornik) N.S. vol. 5 (1939) pp. 317-328. MR 0002006 (1:335b)

[29]

J. J. Stoker, Unbounded convex point sets, Amer. J. Math. vol. 62 (1940) pp. 165-179. MR 0001029 (1:168f)

[30]

M. H. Stone, Notes on Integration. II, Proc. Nat. Acad. Sci. U. S. A. vol. 34 (1948) pp. 447-455. MR 0026102 (10:107b)

[31]

A. Tychonoff, Ein Fixpunktsatz, Math. Ann. vol. 111 (1935) pp. 767-776. MR 1513031