Geodesic
Concerning Non-Planar Circle-Like Continua
Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 242-250

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper it is proved that if a circle-like continuum M cannot be embedded in the plane, then M is not a continuous image of any plane continuum (Theorem 5).Suppose that (S, ρ) is a metric space. A finite sequence of domains L1, L2 , ... , Ln is called a linear chain provided Li intersects Lj if and only if |i — j| ⩽ 1. If, in addition, there is a positive number ∊ such that, for each i, the diameter of Li is less than ∊, then the linear chain is called a linear ∊-chain. If for each positive number ∊ the continuum M can be covered by a linear ∊-chain, then M is said to be chainable (or snake-like) (2). 
Ingram, W. T. Concerning Non-Planar Circle-Like Continua. Canadian journal of mathematics, Tome 19 (1967) no. 1, pp. 242-250. doi: 10.4153/CJM-1967-016-3
@article{10_4153_CJM_1967_016_3,
     author = {Ingram, W. T.},
     title = {Concerning {Non-Planar} {Circle-Like} {Continua}},
     journal = {Canadian journal of mathematics},
     pages = {242--250},
     year = {1967},
     volume = {19},
     number = {1},
     doi = {10.4153/CJM-1967-016-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-016-3/}
}
TY  - JOUR
AU  - Ingram, W. T.
TI  - Concerning Non-Planar Circle-Like Continua
JO  - Canadian journal of mathematics
PY  - 1967
SP  - 242
EP  - 250
VL  - 19
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-016-3/
DO  - 10.4153/CJM-1967-016-3
ID  - 10_4153_CJM_1967_016_3
ER  - 
%0 Journal Article
%A Ingram, W. T.
%T Concerning Non-Planar Circle-Like Continua
%J Canadian journal of mathematics
%D 1967
%P 242-250
%V 19
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1967-016-3/
%R 10.4153/CJM-1967-016-3
%F 10_4153_CJM_1967_016_3

[1] 1. Bing, R. H., A homogeneous indecomposable plane continuum, Duke Math. J., 15 (1948), 729–742. Google Scholar

[2] 2. Bing, R. H., Snake-like continua, Duke Math. J., 18 (1951), 653–663. Google Scholar

[3] 3. Bing, R. H., Concerning hereditarily indecomposable continua, Pacific J. Math., 1 (1951), 43–51. Google Scholar

[4] 4. Bing, R. H., A simple closed curve is the only homogeneous bounded plane continuum that contains an arc, Can. J. Math., 12 (1960), 209–230. Google Scholar

[5] 5. Bing, R. H., Embedding circle-like continua in the plane, Can. J. Math., 14 (1962), 113–128. Google Scholar

[6] 6. Cook, H., On the most general plane closed point set through which it is possible to pass a pseudo-arc, Fund. Math., 55 (1964), 31–42. Google Scholar

[7] 7. Fearnley, Lawrence, Continuous mappings of the pseudo-arc, doctoral dissertation, University of Utah, Salt Lake City, 1959. Google Scholar

[8] 8. Fearnley, Lawrence, Characterizations of the continuous images of the pseudo-arc, Trans. Amer. Math. Soc., 111 (1964), 380–399. Google Scholar

[9] 9. Fort, M. K., Images of plane continua, Amer. J. Math., 81 (1959), 541–546. Google Scholar

[10] 10. Kelley, J. L., General topology (Princeton, 1955). Google Scholar

[11] 11. Lelek, A., On weakly chainable continua, Fund. Math., 50 (1962), 271–282. Google Scholar

[12] 12. McCord, Michael, Inverse limit systems, doctoral dissertation, Yale University, New Haven, 1963. Google Scholar

[13] 13. Moise, E. E., An indecomposable plane continuum which is homeomorphic to each of its nondegenerate subcontinua, Trans. Amer. Math. Soc., 63 (1948), 581–594. Google Scholar

[14] 14. Moore, R. L., Foundations of point set theory, rev. ed., Amer. Math. Soc. Colloq. Pub., 13 (1962). Google Scholar

Cité par Sources :