Another fixed point theorem for plane continua
HTML articles powered by AMS MathViewer
- by Charles L. Hagopian PDF
- Proc. Amer. Math. Soc. 31 (1972), 627-628 Request permission
Abstract:
A continuum $M$ is said to be $\lambda$ connected if every two points of $M$ can be joined by a hereditarily decomposable subcontinuum of $M$. Here we prove that a bounded plane continuum that does not have infinitely many complementary domains is $\lambda$ connected if and only if its boundary does not contain an indecomposable continuum. It follows that every $\lambda$ connected bounded nonseparating subcontinuum of the plane has the fixed point property.References
- Harold Bell, On fixed point properties of plane continua, Trans. Amer. Math. Soc. 128 (1967), 539–548. MR 214036, DOI 10.1090/S0002-9947-1967-0214036-2
- Charles L. Hagopian, A fixed point theorem for plane continua, Bull. Amer. Math. Soc. 77 (1971), 351–354. MR 273591, DOI 10.1090/S0002-9904-1971-12690-3
- K. Sieklucki, On a class of plane acyclic continua with the fixed point property, Fund. Math. 63 (1968), 257–278. MR 240794, DOI 10.4064/fm-63-3-257-278
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 627-628
- DOI: https://doi.org/10.1090/S0002-9939-1972-0286093-6
- MathSciNet review: 0286093