Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1891–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

Linear topological spaces


Author: D. H. Hyers
Journal: Bull. Amer. Math. Soc. 51 (1945), 1-21
DOI: https://doi.org/10.1090/S0002-9904-1945-08273-1
Errata, Volume 51: Bull. Amer. Math. Soc., Volume 51, Number 12 (1945), 1001--1001
MathSciNet review: 0012205
Full-text PDF

References | Additional Information

References [Enhancements On Off] (What's this?)

  • L. Alaoglu, 1. Weak topologies of normed linear spaces, Ann. of Math. vol. 41 (1940) pp. 252-267. MR 1455
  • P. Alexandroff and H. Hopf, 1. Topologie, vol. I, Berlin, 1935.
  • S. Banach, 1. Opérations linéaires, Warsaw, 1932.
  • Garrett Birkhoff, A note on topological groups, Compositio Math. 3 (1936), 427–430. MR 1556955
  • Garrett Birkhoff, Moore-Smith convergence in general topology, Ann. of Math. (2) 38 (1937), no. 1, 39–56. MR 1503323, https://doi.org/10.2307/1968508
  • G. D. Birkhoff and O. D. Kellogg, Invariant points in function space, Trans. Amer. Math. Soc. 23 (1922), no. 1, 96–115. MR 1501192, https://doi.org/10.1090/S0002-9947-1922-1501192-9
  • S. Bochner and J. von Neumann, Almost periodic functions in groups. II, Trans. Amer. Math. Soc. 37 (1935), no. 1, 21–50. MR 1501777, https://doi.org/10.1090/S0002-9947-1935-1501777-9
  • D. G. Bourgin, 1. Linear topological spaces, Amer. J. Math. vol. 65 (1943) pp. 637-659. MR 9104
  • D. G. Bourgin, 2. Some properties of Banach spaces, Amer. J. Math. vol. 64 (1942) pp. 597-612. MR 8116
  • M. M. Day, 1. The spaces L 0<p<1, Bull. Amer. Math. Soc. vol. 46 (1940) pp. 816-823. MR 2700
  • M. M. Day, 2. A property of Banach spaces, Duke Math. J. vol. 8 (1941) pp. 763-770. MR 5776
  • M. Eidelheit and S. Mazur, 1. Eine Bemerkung über die Raume von Typus (F), Studia Mathematica vol. 7 (1938) pp. 159-161.
  • G. Fichtenholz, 1. Sur les fonctionelles linéaires, continues au sens généralisé, Rec. Math. (Math. Sbornik) N.S. vol. 4 (1938) pp. 192-213.
  • M. Fréchet, 1. La differentielle dans l'analyse générale, Ann. École Norm. vol. 42 (1925) pp. 293-323.
  • Maurice Fréchet, Les espaces abstraits topologiquement affines, Acta Math. 47 (1926), no. 1-2, 25–52 (French). MR 1555210, https://doi.org/10.1007/BF02544107
  • M. Fréchet, 3. Les espaces abstraits, Paris, 1928.
  • H. H. Goldstine, Weakly complete Banach spaces, Duke Math. J. 4 (1938), no. 1, 125–131. MR 1546039, https://doi.org/10.1215/S0012-7094-38-00410-7
  • L. M. Graves, 1. Topics in the functional calculus, Bull. Amer. Math. Soc. vol. 41 (1935) pp. 641-662.
  • Lawrence M. Graves, On the completing of a Hausdorff space, Ann. of Math. (2) 38 (1937), no. 1, 61–64. MR 1503325, https://doi.org/10.2307/1968510
  • T. H. Hildebrandt and Lawrence M. Graves, Implicit functions and their differentials in general analysis, Trans. Amer. Math. Soc. 29 (1927), no. 1, 127–153. MR 1501380, https://doi.org/10.1090/S0002-9947-1927-1501380-6
  • D. H. Hyers, 1. Integrals and functional equations in linear topological spaces, California Institute of Technology thesis, 1937.
  • D. H. Hyers, 2. On functional equations in linear topological spaces, Proc. Nat. Acad. Sci. U.S.A. vol. 23 (1937) pp. 496-499.
  • D. H. Hyers, 3. A note on linear topological spaces, Bull. Amer. Math. Soc. vol. 44 (1938) pp. 76-80. MR 12205
  • D. H. Hyers, 4. Locally bounded linear topological spaces, Revista de Ciencias vol. 41 (1939) pp. 555-574. MR 1915
  • D. H. Hyers, 5. Pseudo-normed linear spaces and Abelian groups, Duke Math. J. vol. 5 (1939) pp. 628-634. MR 348
  • D. H. Hyers, 6. A generalization of Fréchet's differential, Proc. Nat. Acad. Sci. U.S.A. vol. 27 (1941) pp. 315-316. MR 4714
  • R. C. James, 1. Linearly arc-wise connected topological Abelian groups, Ann. of Math. vol. 44 (1943) pp. 93-102. MR 7978
  • R. C. James, 2. Topological groups as subgroups of linear topological spaces, Duke Math. J. vol. 10 (1943) pp. 441-453. MR 8818
  • A. Kolmogoroff, 1. Zur Normierbarkeit eines topologischen linearen Raumes, Studia Mathematica vol. 5 (1934) pp. 29-33.
  • J. P. LaSalle, 1. Pseudo-normed linear sets over valued rings, California Institute of Technology Thesis, 1941.
  • J. P. LaSalle, 2. Pseudo-normed linear spaces, Duke Math. J. vol. 8 (1941) pp. 131-136. MR 3447
  • J. P. LaSalle, 3. Topology based upon the concept of a pseudo-norm, Proc. Nat. Acad. Sci. U.S.A. vol 27 (1941) pp. 448-457. MR 4749
  • G. W. Mackey, 1. On infinite dimensional linear spaces, Proc. Nat. Acad. Sci. U.S.A. vol. 29 (1943) pp. 216-221. MR 8638
  • G. W. Mackey, 2. On convex topological linear spaces, Proc. Nat. Acad. Sci. U.S.A. vol. 29 (1943) pp. 315-319. MR 9087
  • S. Mazur and W. Orlicz, 1. Über Folgen linearen Operationen, Studia Mathematica vol. 4 (1933) pp. 152-157.
  • A. D. Michal, 1. Differential calculus in linear topological spaces, Proc. Nat. Acad. Sci. U.S.A. vol. 24 (1938) pp. 340-342.
  • A. D. Michal, 2. General differential geometries and related topics, Bull. Amer. Math. Soc. vol. 45 (1939) pp. 529-563. MR 172
  • A. D. Michal, 3. Differentials of functions with arguments and values in topological abelian groups, Proc. Nat. Acad. Sci. U.S.A. vol. 26 (1940) pp. 356-359. MR 2705
  • A. D. Michal, 4. First order differentials of functions with arguments and values in topological abelian groups, Revista de Ciencias (in press).
  • A. D. Michal, 5. Higher order differentials of functions with arguments and values in topological abelian groups, Revista de Ciencias vol. 42 (1940) pp. 155-177. MR 4715
  • A. D. Michal and E. W. Paxson, 1. La differentielle dans les espaces abstraits linéaires avec une topologie, C. R. Acad. Sci. Paris vol. 202 (1936) pp. 1741-1743.
  • A. D. Michal and E. W. Paxson, 2. The differential in abstract linear spaces with a topology, Comptes Rendus des Séances de la Société des Sciences et des Lettres de Varsovie vol. 29 (1936) pp. 106-121.
  • K. Millsaps, 1. Differential calculus in topological groups, Revista de Ciencias vol. 44 (1942) pp. 485-492. MR 10783
  • K. Millsaps, 2. Differential calculus in topological groups II, Revista de Ciencias vol. 45 (1943) pp. 45-52. MR 10784
  • E. H. Moore and H. L. Smith, A General Theory of Limits, Amer. J. Math. 44 (1922), no. 2, 102–121. MR 1506463, https://doi.org/10.2307/2370388
  • E. W. Paxson, 1. Analysis in linear topological spaces, California Institute of Technology Thesis, 1937.
  • E. W. Paxson, 2. Sur un espace fonctionnel abstrait, Revista de Ciencias vol. 42 (1940) pp. 817-822. MR 4074
  • E. W. Paxson, 3. Les équations differentielles dans les espaces linéaires et topologiques, Revista de Ciencias vol. 42 (1940) pp. 823-826. MR 4075
  • E. W. Paxson, 4. Linear topological groups, Ann. of Math. vol. 40 (1938) pp. 575-580.
  • R. S. Phillips, 1. Integration in a convex linear topological space, Trans. Amer. Math. Soc. vol. 47 (1940) pp. 114-145. MR 2707
  • E. J. Pinney, 1. The calculus of variations in abstract spaces and related topics, California Institute of Technology Thesis, 1942.
  • L. Pontrjagin, 1. Topological groups, Princeton, 1939.
  • Friedrich Riesz, Über lineare Funktionalgleichungen, Acta Math. 41 (1916), no. 1, 71–98 (German). MR 1555146, https://doi.org/10.1007/BF02422940
  • J. Schauder, 1. Der Fixpunktsatz in Funktionalraumen, Studia Mathematica vol. 2, pp. 171-180.
  • V. Šmulian, 1. Linear topological spaces and their connection with Banach spaces, C. R. (Doklady) Acad. Sci. URSS. vol. 22 (1939) pp. 471-473.
  • A. E. Taylor, 1. The weak topologies of Banach spaces, Proc. Nat. Acad. Sci. U.S.A. vol. 25 (1939) pp. 438-440. MR 652
  • A. E. Taylor, 2. The weak topologies of Banach spaces, Revista de Ciencias vol. 43 (1941) pp. 355-365, 465-474, 667-674 and vol. 44 (1942) pp. 45-63. MR 6602
  • J. Tukey, 1. Convergence and uniformity in topology, Princeton, 1940. MR 2515
  • John von Neumann, On complete topological spaces, Trans. Amer. Math. Soc. 37 (1935), no. 1, 1–20. MR 1501776, https://doi.org/10.1090/S0002-9947-1935-1501776-7
  • J. von Neumann, 2. Zur Algebra der Funktionaloperatoren und theorie der normalen Operatoren, Math. Ann. vol. 102 (1929) pp. 370-427.
  • A. Tychonoff, Ein Fixpunktsatz, Math. Ann. 111 (1935), no. 1, 767–776 (German). MR 1513031, https://doi.org/10.1007/BF01472256
  • John V. Wehausen, Transformations in linear topological spaces, Duke Math. J. 4 (1938), no. 1, 157–169. MR 1546041, https://doi.org/10.1215/S0012-7094-38-00412-0
  • A. Weil, 1. Sur les espaces à structure uniforme, Actualités Scientifiques et Industrielles, No. 551, Paris, 1938.
  • H. Weyl, 1. On the differential equation of the simplest boundary layer problems, Ann. of Math. vol. 43 (1942) pp. 381-407. MR 6294

Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1945-08273-1