|
Partitioning continuous curves
Author:
R. H. Bing
Journal:
Bull. Amer. Math. Soc. 58 (1952), 536-556
MathSciNet review:
0049550
Full-text PDF
References |
Additional Information
- 1.
Gustav Beer, Beweis des Satzes, dass jede im kleinen zusammenhängende Kurve convex metrisiert werden kann, Fund. Math. vol. 31 (1938) pp. 281-320.
- 2.
R.
H. Bing, A characterization of 3-space by
partitionings, Trans. Amer. Math. Soc. 70 (1951), 15–27. MR 0044827
(13,484c), http://dx.doi.org/10.1090/S0002-9947-1951-0044827-0
- 3.
R.
H. Bing, A convex metric for a locally
connected continuum, Bull. Amer. Math. Soc.
55 (1949),
812–819. MR 0031712
(11,194d), http://dx.doi.org/10.1090/S0002-9904-1949-09298-4
- 4.
R.
H. Bing, Complementary domains of continuous curves, Fund.
Math. 36 (1949), 303–318. MR 0038063
(12,348h)
- 5.
R.
H. Bing, Higher-dimensional hereditarily
indecomposable continua, Trans. Amer. Math.
Soc. 71 (1951),
267–273. MR 0043452
(13,265c), http://dx.doi.org/10.1090/S0002-9947-1951-0043452-5
- 6.
R.
H. Bing, Partitioning a set, Bull. Amer. Math. Soc. 55 (1949), 1101–1110. MR 0035429
(11,733i), http://dx.doi.org/10.1090/S0002-9904-1949-09334-5
- 7.
R.
H. Bing, The Kline sphere characterization
problem, Bull. Amer. Math. Soc. 52 (1946), 644–653. MR 0016645
(8,46h), http://dx.doi.org/10.1090/S0002-9904-1946-08614-0
- 8.
R.
H. Bing and E.
E. Floyd, Coverings with connected
intersections, Trans. Amer. Math. Soc. 69 (1950), 387–391.
MR
0043453 (13,265d), http://dx.doi.org/10.1090/S0002-9947-1950-0043453-6
- 9.
L. M. Blumenthal, Distance geometries, University of Missouri Studies, vol. 13, No. 2, 1938.
- 10.
Orville
G. Harrold Jr., Concerning the Convexification of Continuous
Curves, Amer. J. Math. 61 (1939), no. 1,
210–216. MR
1507372, http://dx.doi.org/10.2307/2371400
- 11.
Witold
Hurewicz and Henry
Wallman, Dimension Theory, Princeton Mathematical Series, v.
4, Princeton University Press, Princeton, N. J., 1941. MR 0006493
(3,312b)
- 12.
C. Kuratowski and G. T. Whyburn, Sur les éléments cycliques et leurs applications, Fund. Math. vol. 16 (1930) pp. 305-331.
- 13.
Solomon
Lefschetz, Algebraic Topology, American Mathematical Society
Colloquium Publications, v. 27, American Mathematical Society, New York,
1942. MR
0007093 (4,84f)
- 14.
Karl
Menger, Untersuchungen über allgemeine Metrik, Math. Ann.
100 (1928), no. 1, 75–163 (German). MR
1512479, http://dx.doi.org/10.1007/BF01448840
- 15.
Edwin
E. Moise, Grille decomposition and
convexification theorems for compact metric locally connected
continua, Bull. Amer. Math. Soc. 55 (1949), 1111–1121. MR 0035430
(11,734a), http://dx.doi.org/10.1090/S0002-9904-1949-09336-9
- 16.
Edwin
E. Moise, A note of correction, Proc. Amer. Math. Soc. 2 (1951), 838. MR 0043454
(13,265e), http://dx.doi.org/10.1090/S0002-9939-1951-0043454-4
- 17.
R. L. Moore, Concerning connectedness im kleinen and a related property, Fund. Math. vol. 3 (1922) pp. 232-237.
- 18.
R.
L. Moore, Foundations of point set theory, Revised edition.
American Mathematical Society Colloquium Publications, Vol. XIII, American
Mathematical Society, Providence, R.I., 1962. MR 0150722
(27 #709)
- 19.
W. Sierpinski, Sur une condition pour qu'un continu soit une courbe jordanienne, Fund. Math. vol. 1 (1920) pp. 44-60.
- 20.
Garth Thomas, Simultaneous partitionings, Bull. Amer. Math. Soc. Abstracts 57-4-366 and 57-6-553.
- 21.
Gordon
Thomas Whyburn, Analytic Topology, American Mathematical
Society Colloquium Publications, v. 28, American Mathematical Society, New
York, 1942. MR
0007095 (4,86b)
- 22.
G. T. Whyburn, Concerning S-regions in locally connected continua, Fund. Math. vol. 20 (1933) pp. 131-139.
- 23.
G.
T. Whyburn, The existence of certain transformations, Duke
Math. J. 5 (1939), 647–655. MR 0000178
(1,30d)
- 24.
Raymond
Louis Wilder, Topology of Manifolds, American Mathematical
Society Colloquium Publications, vol. 32, American Mathematical Society,
New York, N. Y., 1949. MR 0029491
(10,614c)
- 25.
Leo
Zippin, On Continuous Curves and the Jordan Curve Theorem,
Amer. J. Math. 52 (1930), no. 2, 331–350. MR
1506758, http://dx.doi.org/10.2307/2370687
- 1.
- Gustav Beer, Beweis des Satzes, dass jede im kleinen zusammenhängende Kurve convex metrisiert werden kann, Fund. Math. vol. 31 (1938) pp. 281-320.
- 2.
- R. H. Bing, A characterization of 3-space by partitionings, Trans. Amer. Math. Soc. vol. 70 (1951) pp. 15-17. MR 44827
- 3.
- R. H. Bing, A convex metric for a locally connected continuum, Bull. Amer. Math. Soc. vol. 55 (1949) pp. 812-819. MR 31712
- 4.
- R. H. Bing, Complementary domains of continuous curves, Fund. Math. vol. 36 (1949) pp. 306-318. MR 38063
- 5.
- R. H. Bing, Higher dimensional hereditarily indecomposable continua, Trans. Amer. Math. Soc. vol. 71 (1951) pp. 267-273. MR 43452
- 6.
- R. H. Bing, Partitioning a set, Bull. Amer. Math. Soc. vol. 55 (1949) pp. 1101-1110. MR 35429
- 7.
- R. H. Bing, The Kline sphere characterization problem, Bull. Amer. Math. Soc. vol. 52 (1946) pp. 644-653. MR 16645
- 8.
- R. H. Bing and E. E. Floyd, Coverings with connected intersections, Trans. Amer. Math. Soc. vol. 69 (1950) pp. 387-391. MR 43453
- 9.
- L. M. Blumenthal, Distance geometries, University of Missouri Studies, vol. 13, No. 2, 1938.
- 10.
- O. G. Harrold, Jr., Concerning the convexification of continuous curves, Amer. J. Math. vol. 61 (1930) pp. 210-216. MR 1507372
- 11.
- W. Hurewicz and H. Wallman, Dimension theory, Princeton University Press, 1948. MR 6493
- 12.
- C. Kuratowski and G. T. Whyburn, Sur les éléments cycliques et leurs applications, Fund. Math. vol. 16 (1930) pp. 305-331.
- 13.
- S. Lefschetz, Algebraic topology, Amer. Math. Soc. Colloquium Publications, vol. 27, New York, 1942. MR 7093
- 14.
- K. Menger, Untersuchungen über allgemeine Metrik, Math. Ann. vol. 100 (1928) pp. 75-163. MR 1512479
- 15.
- E. E. Moise, Grille decomposition and convexification theorems for compact metric locally connected continua, Bull. Amer. Math. Soc. vol. 55 (1949) pp. 1111-1121. MR 35430
- 16.
- E. E. Moise, A note of correction, Proceedings of the American Mathematical Society vol. 2 (1951) p. 838. MR 43454
- 17.
- R. L. Moore, Concerning connectedness im kleinen and a related property, Fund. Math. vol. 3 (1922) pp. 232-237.
- 18.
- R. L. Moore, Foundations of point set theory, Amer. Math. Soc. Colloquium Publications, vol. 13, New York, 1932. MR 150722
- 19.
- W. Sierpinski, Sur une condition pour qu'un continu soit une courbe jordanienne, Fund. Math. vol. 1 (1920) pp. 44-60.
- 20.
- Garth Thomas, Simultaneous partitionings, Bull. Amer. Math. Soc. Abstracts 57-4-366 and 57-6-553.
- 21.
- G. T. Whyburn, Analytic topology, Amer. Math. Soc. Colloquium Publications, vol. 28, New York, 1942. MR 7095
- 22.
- G. T. Whyburn, Concerning S-regions in locally connected continua, Fund. Math. vol. 20 (1933) pp. 131-139.
- 23.
- G. T. Whyburn, The existence of certain transformations, Duke Math. J. vol. 5 (1939) pp. 647-655. MR 178
- 24.
- R. L. Wilder, Topology of manifolds, Amer. Math. Soc. Colloquium Publications, vol. 32, New York, 1949. MR 29491
- 25.
- L. Zippin, On continuous curves and the Jordan curve theorem, Amer. J. Math. vol. 52 (1930) pp. 331-350. MR 1506758
Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1952-09621-X
PII:
S 0002-9904(1952)09621-X
|
