Bourgin, D. G. Classes of transformation \(s\) and bordering transformations. (English) Zbl 0043.32902 Bull. Am. Math. Soc. 57, 223-237 (1951). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 206 Documents Keywords:functional analysis PDF BibTeX XML Cite \textit{D. G. Bourgin}, Bull. Am. Math. Soc. 57, 223--237 (1951; Zbl 0043.32902) Full Text: DOI References: [1] N. Aronszajn, Caractérisation métrique de l’espace de Hilbert, des espaces vectorieles et de certains groupes métriques, C.R. Acad. Sci. Paris vol. 201 (1935) pp. 811-813 and 873-875. · JFM 61.0633.01 [2] N. Aronszajn, Le correspondant topologique de l’unicité dans la théorie des équations différentielles, Ann. of Math. (2) 43 (1942), 730 – 738 (French). · Zbl 0061.17106 [3] S. Banach, Théorie des opérations linéaires, Warsaw, 1932. · JFM 58.0420.01 [4] D. G. Bourgin, Approximate isometries, Bull. Amer. Math. Soc. 52 (1946), 704 – 714. · Zbl 0060.26405 [5] D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385 – 397. · Zbl 0033.37702 [6] D. G. Bourgin, Multiplicative transformations, Proc. Nat. Acad. Sci. U. S. A. 36 (1950), 564 – 570. · Zbl 0039.33403 [7] D. G. Bourgin, A class of sequences of functions, Trans. Amer. Math. Soc. 60 (1946), 478 – 518. · Zbl 0061.13404 [8] D. G. Bourgin and C. W. Mendel, Orthonormal sets of periodic functions of the type {\?(\?\?)}, Trans. Amer. Math. Soc. 57 (1945), 332 – 363. · Zbl 0060.17107 [9] D. G. Bourgin and A. Charnes, Unpublished. [10] F. Browder, Thesis, Princeton University. [11] C. H. Dowker, An extension of Alexandroff’s mapping theorem, Bull. Amer. Math. Soc. 54 (1948), 386 – 391. · Zbl 0034.25601 [12] S. Eilenberg, Sur les groupes compacts d’homéomorphie, Fund. Math. vol. 28 (1937) pp. 75-80. · Zbl 0015.24805 [13] R. Fortet, Remarques sur les espaces uniformément convexes, Bull. Soc. Math. France 69 (1941), 23 – 46 (French). · Zbl 0026.32401 [14] Paul R. Halmos, Comment on the real line, Bull. Amer. Math. Soc. 50 (1944), 877 – 878. · Zbl 0061.04404 [15] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A. 27 (1941), 222 – 224. · Zbl 0061.26403 [16] D. H. Hyers and S. M. Ulam, On approximate isometries, Bull. Amer. Math. Soc. 51 (1945), 288 – 292. · Zbl 0060.26404 [17] D. H. Hyers and S. M. Ulam, Approximate isometries of the space of continuous functions, Ann. of Math. (2) 48 (1947), 285 – 289. · Zbl 0029.36701 [18] D. H. Hyers and S. Ulam, Unpublished. [19] Loo-Keng Hua, On the automorphisms of a sfield, Proc. Nat. Acad. Sci. U. S. A. 35 (1949), 386 – 389. · Zbl 0033.10402 [20] Shizuo Kakutani, Topological properties of the unit sphere of a Hilbert space, Proc. Imp. Acad. Tokyo 19 (1943), 269 – 271. · Zbl 0060.27701 [21] Solomon Lefschetz, Algebraic Topology, American Mathematical Society Colloquium Publications, v. 27, American Mathematical Society, New York, 1942. · Zbl 0061.39302 [22] Solomon Lefschetz, Topics in Topology, Annals of Mathematics Studies, no. 10, Princeton University Press, Princeton, N. J., 1942. · Zbl 0061.39303 [23] Jean Leray, Sur la forme des espaces topologiques et sur les points fixes des représentations, J. Math. Pures Appl. (9) 24 (1945), 95 – 167 (French). · Zbl 0060.40703 [24] Jean Leray, Sur la position d’un ensemble fermé de points d’un espace topologique, J. Math. Pures Appl. (9) 24 (1945), 169 – 199 (French). · Zbl 0060.40704 [25] Jean Leray, Sur les équations et les transformations, J. Math. Pures Appl. (9) 24 (1946), 201 – 248 (French). · Zbl 0060.40705 [26] Jean Leray and Jules Schauder, Topologie et équations fonctionnelles, Ann. Sci. École Norm. Sup. (3) 51 (1934), 45 – 78 (French). · Zbl 0009.07301 [27] A. Lindenbaum, Contributions a l’étude de l’espace métrique I, Fund. Math. vol. 8 (1926) pp. 209-222. · JFM 52.0585.01 [28] S. Mazur and S. Ulam, Sur les transformations isométrique d’espaces vectoriels, normés, C.R. Acad. Sci. Paris vol. 194 (1932) pp. 946-948. · Zbl 0004.02103 [29] T. Nakayama, Unpublished. [30] J. Nielsen, Untersuchungen zur Topologie der geschlossen zweiseitigen Fläche, I, Acta. Math. vol. 50 (1927) pp. 189-358; II, vol. 53 (1929) pp. 1-76; III, vol. 58 (1932) pp. 87-167. · JFM 53.0545.12 [31] Kurt Reidemeister, Automorphismen von Homotopiekettenringen, Math. Ann. 112 (1936), no. 1, 586 – 593 (German). · Zbl 0013.36903 [32] Erich Rothe, The theory of topological order in some linear topological spaces, Iowa State Coll. J. Sci. 13 (1939), 373 – 390. · Zbl 0022.41201 [33] Wladimir Seidel, On the distribution of values of bounded analytic functions, Trans. Amer. Math. Soc. 36 (1934), no. 1, 201 – 226. · Zbl 0008.36303 [34] M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), no. 3, 375 – 481. · Zbl 0017.13502 [35] R. L. Swain, Unpublished. [36] Franz Wecken, Fixpunktklassen. I, Math. Ann. 117 (1941), 659 – 671 (German). · Zbl 0024.08405 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.