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The mathematical work of R. L. Moore: Its background, nature and influence

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Publications of R. L. Moore

  1. Geometry in which the sum of the angles of every triangle is two right angles, Trans. Amer. Math. Soc. 8 (1907), 369–378.

  2. Sets of metrical hypotheses for geometry, Trans. Amer. Math. Soc. 9 (1908), 487–512.

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  3. A note concerning Veblen's axioms for geometry, Trans. Amer. Math. Soc. 13 (1912), 74–78.

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  4. On Duhamel's theorem, Ann. of Math. 13 (1912), 161–168.

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  5. On a set of postulates which suffice to define a number-plane, Trans. Amer. Math. Soc. 16 (1915), 27–32.

  6. The linear continuum in terms of point and limit, Ann. of Math. 16 (1915), 123–133.

  7. On the linear continuum, Bull. Amer. Math. Soc. 22 (1915), 117–122.

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  8. Concerning a non-metrical pseudo-Archimedean axiom, Bull. Amer. Math. Soc. 22 (1916), 225–236.

  9. On the foundations of plane analysis situs, Proc. Nat. Acad. Sci. U.S.A. 2 (1916), 270–272.

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  10. On the foundations of plane analysis situs, Trans. Amer. Math. Soc. 17 (1916), 131–164.

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  11. A theorem concerning continuous curves, Bull. Amer. Math. Soc. 23 (1917), 233–236.

  12. A characterization of Jordan regions by properties having no reference to their boundaries, Proc. Nat. Acad. Sci. U.S.A. 4 (1918), 364–370.

  13. Continuous curves that have no continuous sets of condensation, Bull. Amer. Math. Soc. 20 (1919), 174–176.

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  14. Concerning a set of postulates for plane analysis situs, Trans. Amer. Math. Soc. 20 (1919), 169–178.

  15. (With J. R. Kline) On the most general plane closed point set through which it is possible to pass a simple continuous arc, Ann. of Math. 20 (1919), 218–223.

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  16. On the most general class L of Fréchet in which the Heine-Borel-Lebesgue theorem holds true, Proc. Nat. Acad. Sci. U.S.A. 5 (1919), 206–210.

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  17. On the Lie-Riemann-Helmholtz-Hilbert problem of the foundations of geometry, Amer. Jour. Math. 41 (1919), 299–319.

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  18. The second volume of Veblen and Young's projective geometry, Bull. Amer. Math. Soc. 26 (1920), 412–425 (book review).

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  19. Concerning simple continuous curves, Trans. Amer. Math. Soc. 21 (1920), 333–347.

  20. Concerning certain equicontinuous systems of curves, Trans. Amer. Math. Soc. 22 (1921), 41–45.

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  21. On the relation of a continuous curve to its complementary domains in space of three dimensions, Proc. Nat. Acad. Sci. U.S.A. 8 (1922), 33–38.

  22. Concerning connectedness im kleinen and a related property, Fund. Math. 3 (1922), 232–237.

  23. Concerning continuous curves in the plane, Math. Zeit. 15 (1922), 254–260.

  24. On the generation of a simple surface by means of a set of equicontinuous curves, Fund. Math. 4 (1923), 106–117.

  25. An uncountable, closed and non-dense point set each of whose complementary intervals abuts on another one at each of its ends, Bull. Amer. Math. Soc. 29 (1923), 49–50.

  26. Concerning the cut-points of continuous curves and of other closed and connected point-sets, Proc. Nat. Acad. Sci. U.S.A. 9 (1923), 101–106.

  27. Report on continuous curves from the viewpoint of analysis situs, Bull. Amer. Math. Soc. 29 (1923), 289–302.

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  28. An extension of the theorem that no countable point set is perfect, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 168–170.

  29. Concerning the prime parts of certain continua which separate the plane, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 170–175.

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  30. Concerning relatively uniform convergence, Bull. Amer. Math. Soc. 30 (1924), 504–505.

  31. Concerning the sum of a countable number of mutually exclusive continua in the plane, Fund. Math. 6 (1924), 189–202.

  32. Concerning upper semi-continuous collections of continua which do not separate a given continuum, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 356–360.

  33. Concerning the common boundary of two domains, Fund. Math. 6 (1924), 203–213.

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  34. Concerning sets of segments which cover a point set in the Vitali sense, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 464–467.

  35. Concerning the prime parts of a continuum, Math. Zeit. 22 (1925), 307–315.

  36. A characterization of a continuous curve, Fund. Math. 7 (1925), 302–307.

  37. Concerning the separation of points sets by curves, Proc. Nat. Acad. Sci. U.S.A. 11 (1926), 469–476.

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  38. Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc. 27 (1925), 416–428.

  39. Concerning the relation between separability and the proposition that every uncountable point set has a limit point, Fund. Math. 8 (1926), 189–192; also, An acknowledgement, ibid., 374–375.

  40. Conditions under which one of two given closed linear point sets may be thrown into the other one by a continuous transformation of a plane into itself, Amer. Jour. Math. 48 (1926), 67–72.

  41. Concerning indecomposable continua and continua which contain no subsets that separate the plane, Proc. Nat. Acad. Sci. U.S.A. 12 (1926), 359–363.

  42. Covering theorems, Bull. Amer. Math. Soc. 32 (1926), 275–282.

  43. A connected and regular point set which contains no arc, Bull. Amer. Math. Soc. 32 (1926), 331–332.

  44. Concerning paths that do not separate a given continuous curve, Proc. Nat. Acad. Sci. U.S.A. 12 (1926), 745–753.

  45. Some separation theorems, Proc. Nat. Acad. Sci. U.S.A. 13 (1927), 711–716.

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  46. Concerning triods in the plane and the junction points of plane continua, Proc. Nat. Acad. U.S.A. 14 (1928), 85–88.

  47. On the separation of the plane by a continuum, Bull. Amer. Math. Soc. 34 (1928), 303–306.

  48. A separation theorem, Fund. Math. 12 (1928), 295–297.

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  49. Concerning triodic continua in the plane, Fund. Math. 13 (1929), 261–263.

  50. Concerning upper semi-continuous collections, Monatsh. Math. Phys. 36 (1929), 81–88.

  51. Foundations of point set theory, Amer. Math. Soc. Coll. Pub., vol. 13, Amer. Math. Soc., Providence, R.I., 1932; rev. ed. 1962; reprinted with corrections, 1970.

  52. Concerning compact continua which contain no continuum that separates the plane, Proc. Nat. Acad. Sci. U.S.A. 20 (1934), 41–45.

  53. A set of axioms for plane analysis situs, Fund. Math. 25 (1935), 13–28.

  54. Foundations of a point set theory in which some points are contiguous to others, Rice Institute Pamphlet 23 (1936), 1–41.

  55. Upper semi-continuous collections of the second type, Rice Institute Pamphlet 23 (1936), 42–57.

  56. On the structure of continua, Rice Institute Pamphlet 23 (1936), 58–74.

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  57. Concerning essential continua of condensation, Trans. Amer. Math. Soc. 42 (1937), 41–52.

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  58. Concerning accessibility, Proc. Nat. Acad. Sci. U.S.A. 25 (1939), 648–653.

  59. Concerning the open subsets of a plane continuum, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 24–25.

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  60. Concerning separability, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 56–58.

  61. Concerning intersecting continua, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 544–550.

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  62. Concerning a continuum and its boundary, Proc. Nat. Acad. U.S.A. 28 (1942), 550–555.

  63. Concerning domains whose boundaries are compact, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 555–561.

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  64. Concerning continua which have dendratomic subsets, Proc. Nat. Acad. Sci. U.S.A. 29 (1943), 384–389.

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  65. Concerning webs in the plane, Proc. Nat. Acad. Sci. U.S.A. 29 (1943), 389–393.

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  66. Concerning tangents to continua in the plane, Proc. Nat. Acad. Sci. U.S.A. 31 (1945), 67–70.

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  67. A characterization of a simple plane web, Proc. Nat. Acad. Sci. U.S.A. 32 (1946), 311–316.

  68. Spirals in the plane, Proc. Nat. Acad. Sci. U.S.A. 39 (1953), 207–213.

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  1. University of California, Santa Barbara

    R. L. Wilder

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  1. R. L. Wilder
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Communicated by C. Truesdell

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Wilder, R.L. The mathematical work of R. L. Moore: Its background, nature and influence. Arch. Hist. Exact Sci. 26, 73–97 (1982). https://doi.org/10.1007/BF00348310

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