Geodesic
Small Compact Actions on Chainable Continua
Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 563-575

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

1. Introduction. In 1931, Newman [9] showed that a connected manifold cannot accept arbitrarily small period-n homeomorphisms, for any n > 1. In this paper we are concerned with the existence of chainable continua with arbitrarily small homeomorphisms.For a long time the only known periodic homeomorphisms of chainable continua had periods 1, 2 or 4 [4]. Recently, Wayne Lewis [8] showed that the pseudo-arc admits periodic homeomorphisms of every order, as well as p-adic cantor group actions. We will see that such homeomorphisms can be made arbitrarily small.In Section 4, a different chainable indecomposable continuum accepting arbitrarily small period-2 homeomorphisms is constructed. 
Toledo, Juan A. Small Compact Actions on Chainable Continua. Canadian journal of mathematics, Tome 38 (1986) no. 3, pp. 563-575. doi: 10.4153/CJM-1986-028-8
@article{10_4153_CJM_1986_028_8,
     author = {Toledo, Juan A.},
     title = {Small {Compact} {Actions} on {Chainable} {Continua}},
     journal = {Canadian journal of mathematics},
     pages = {563--575},
     year = {1986},
     volume = {38},
     number = {3},
     doi = {10.4153/CJM-1986-028-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1986-028-8/}
}
TY  - JOUR
AU  - Toledo, Juan A.
TI  - Small Compact Actions on Chainable Continua
JO  - Canadian journal of mathematics
PY  - 1986
SP  - 563
EP  - 575
VL  - 38
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1986-028-8/
DO  - 10.4153/CJM-1986-028-8
ID  - 10_4153_CJM_1986_028_8
ER  - 
%0 Journal Article
%A Toledo, Juan A.
%T Small Compact Actions on Chainable Continua
%J Canadian journal of mathematics
%D 1986
%P 563-575
%V 38
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1986-028-8/
%R 10.4153/CJM-1986-028-8
%F 10_4153_CJM_1986_028_8

[1] 1. Arens, R., Topologies for homeomorphism groups, Amer. J. Math. 68 (1946), 593–610. Google Scholar

[2] 2. Bing, R. H., A homogeneous indecomposable plane continuum, Duke Math. J. 75 (1948), 729–742. Google Scholar

[3] 3. Bing, R. H. and Jones, F. B., Another homogeneous indecomposable continuum, Trans. Amer. Math. Soc. 90 (1959), 171–192. Google Scholar

[4] 4. Brechner, B. L., Periodic homeomorphisms on chainable continua, Fund. Math. 64 (1969), 197–202. Google Scholar

[5] 5. Hu, S., Elements of general topology (Holden Day, 1964). Google Scholar

[6] 6. Ingram, T. and Cook, H., A characterization of compact indecomposable continua, Arizona State University Topology Conference (1967), 168–169. Google Scholar

[7] 7. Kelley, J. L., General topology (Van Nostrand, 1955). Google Scholar

[8] 8. Lewis, W., Periodic homeomorphisms of chainable continua, Fund. Math. 117 (1983), 81–84. Google Scholar

[9] 9. Newman, M. H. A., A theorem on periodic transformations of spaces, Quarterly J. of Math. 2 (1931), 1–8. Google Scholar

[10] 10. Rosenholtz, I., Open maps of chainable continua, Proc. Amer. Math. Soc. 42 (1974), 258–264. Google Scholar

Cité par Sources :