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Disks in . I. Subsets of disks having neighborhoods lying on -spheres
Author:
Ralph J. Bean
Journal:
Trans. Amer. Math. Soc. 112 (1964), 206-213
MSC:
Primary 54.78
MathSciNet review:
0162235
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
- [1]
J. W. Alexander, An example of a simply connected surface bounding a region which is not simply connected, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 8-10.
- [2]
R.
H. Bing, Approximating surfaces from the side, Ann. of Math.
(2) 77 (1963), 145–192. MR 0150744
(27 #731)
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R.
H. Bing, Approximating surfaces with polyhedral ones, Ann. of
Math. (2) 65 (1957), 465–483. MR 0087090
(19,300f)
- [4]
R.
H. Bing, A surface is tame if its complement is
1-ULC, Trans. Amer. Math. Soc. 101 (1961), 294–305. MR 0131265
(24 #A1117), http://dx.doi.org/10.1090/S0002-9947-1961-0131265-1
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R.
H. Bing, A wild surface each of whose arcs is tame, Duke Math.
J. 28 (1961), 1–15. MR 0123302
(23 #A630)
- [6]
R.
H. Bing, Conditions under which a surface in 𝐸³ is
tame, Fund. Math. 47 (1959), 105–139. MR 0107229
(21 #5954)
- [7]
-, Each disk in
is pierced by a tame arc, Abstract 559-19, Notices Amer. Math. Soc. 6 (1959), 510.
- [8]
R.
H. Bing, Locally tame sets are tame, Ann. of Math. (2)
59 (1954), 145–158. MR 0061377
(15,816d)
- [9]
-, Notes of the topology institute, Univ. of Georgia, Athens, Ga., 1961.
- [10]
Ralph
H. Fox and Emil
Artin, Some wild cells and spheres in three-dimensional space,
Ann. of Math. (2) 49 (1948), 979–990. MR 0027512
(10,317g)
- [11]
Joseph
M. Martin, Extending a disk to a sphere,
Trans. Amer. Math. Soc. 109 (1963), 385–399. MR 0158381
(28 #1606), http://dx.doi.org/10.1090/S0002-9947-1963-0158381-4
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Edwin
E. Moise, Affine structures in 3-manifolds. VIII. Invariance of the
knot-types; local tame imbedding, Ann. of Math. (2)
59 (1954), 159–170. MR 0061822
(15,889g)
- [13]
L.
S. Pontryagin, Foundations of combinatorial topology, Graylock
Press, Rochester, N. Y., 1952. MR 0049559
(14,194b)
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A.
Schoenflies, Beiträge zur Theorie der Punktmengen. III,
Math. Ann. 62 (1906), no. 2, 286–328 (German).
MR
1511377, http://dx.doi.org/10.1007/BF01449982
- [1]
- J. W. Alexander, An example of a simply connected surface bounding a region which is not simply connected, Proc. Nat. Acad. Sci. U.S.A. 10 (1924), 8-10.
- [2]
- R. H. Bing, Approximating surfaces from the side, Ann. of Math. (2) 77 (1963), 145-192. MR 0150744 (27:731)
- [3]
- -, Approximating surfaces with polyhedral ones, Ann. of Math. (2) 65 (1957), 456-483. MR 0087090 (19:300f)
- [4]
- -, A surface is tame if its complement is 1-ULC, Trans. Amer. Math. Soc. 101 (1961), 294-305. MR 0131265 (24:A1117)
- [5]
- -, A wild surface each of whose arcs is tame, Duke Math. J. 28 (1961), 1-16. MR 0123302 (23:A630)
- [6]
- -, Conditions under which a surface in
is tame, Fund. Math. 47 (1959), 105-139. MR 0107229 (21:5954)
- [7]
- -, Each disk in
is pierced by a tame arc, Abstract 559-19, Notices Amer. Math. Soc. 6 (1959), 510.
- [8]
- -, Locally tame sets are tame, Ann. of Math. (2) 59 (1954), 145-158. MR 0061377 (15:816d)
- [9]
- -, Notes of the topology institute, Univ. of Georgia, Athens, Ga., 1961.
- [10]
- R. H. Fox and E. Artin, Some wild cells and spheres in three dimensional space, Ann. of Math. (2) 49 (1948), 979-990. MR 0027512 (10:317g)
- [11]
- Joseph Martin, Disks on spheres, Abstract 584-9, Notices Amer. Math. Soc. 8 (1961), 498 ; Extending a disk on a sphere, Trans. Amer. Math. Soc. 109 (1963), 385-399. MR 0158381 (28:1606)
- [12]
- E. E. Moise, Affine structures in 3-manifolds. VIII, Ann. of Math. (2) 59 (1954), 159-170. MR 0061822 (15:889g)
- [13]
- L. S. Pontryjagin, Foundations of combinatorial topology, Graylock Press, Rochester, N. Y., 1952. MR 0049559 (14:194b)
- [14]
- A. Schoenflies, Beitrage zur Theorie der Punktmengen. III, Math. Ann. 62 (1906), 286-328. MR 1511377
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1964-0162235-8
PII:
S 0002-9947(1964)0162235-8
Article copyright:
© Copyright 1964 American Mathematical Society
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