Unions of chainable continua with the fixed point property

• Autorzy: Hagopian Ch. L. , Marsh M.M.

Identyfikatory

DOI

10.4064/ba210729-30-7

• Języki publikacji: EN

Abstrakty

EN

We investigate the fixed point property for continua that are unions of chainable continua. We answer Question 2 of our paper [Fund. Math. 231 (2013)] by showing the fixed point property is additive for chainable continua. We additionally show that (i) various finite unions of chainable continua have the fixed point property, and (ii) infinite unions of chainable continua that are 1-dimensional, upper semicontinuous clumps as defined by H. Cook have the fixed point property.

Słowa kluczowe

EN

chainable continua; unions of chainable continua; clumps; fixed point property

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2021
• Tom: Vol. 69, no. 1
• Strony: 87--95
• Opis fizyczny: Bibliogr. 16 poz., rys.

Twórcy

autor

Hagopian Ch. L.

• Department of Mathematics & Statistics, California State University, Sacramento, Sacramento, CA 95819-6051, USA

autor

Marsh M.M.

• Department of Mathematics & Statistics, California State University, Sacramento, Sacramento, CA 95819-6051, USA

• https://orcid.org/0000-0002-7472-3389

Bibliografia

• [1] H. Bell, On fixed point properties of plane continua, Trans. Amer. Math. Soc. 128 (1967), 529-548.
• [2] H. Cook, Tree-likeness of dendroids and λ-dendroids, Fund. Math. 68 (1970), 19-22.
• [3] H. Cook, Clumps of continua, Fund. Math. 86 (1974), 91-100.
• [4] C. L. Hagopian and M. M. Marsh, Non-additivity of the fixed point property for tree-like continua, Fund. Math. 231 (2015), 113-137.
• [5] O. H. Hamilton, A fixed point theorem for pseudo-arcs and certain other metric continua, Proc. Amer. Math. Soc. 2 (1951), 173-174.
• [6] W. T. Ingram, Tree-likeness of certain inverse limits with set-valued functions, Topology Proc. 42 (2013), 17-24.
• [7] W. T. Ingram, One-dimensional inverse limits with set-valued functions, Topology Proc. 46 (2015), 243-253.
• [8] W. Lopez, An example in the fixed point theory of polyhedra, Bull. Amer. Math. Soc. 73 (1967), 922-924.
• [9] T. Maćkowiak, Indecomposable continua and the fixed point property, Bull. Acad. Polon. Sci. Sér. Sci. Math. 27 (1979), 903-912.
• [10] R. Mańka, Association and fixed points, Fund. Math. 91 (1976), 105-121.
• [11] R. Mańka, On uniquely arcwise connected curves, Colloq. Math. 51 (1987), 227-238.
• [12] R. Mańka, On the additivity of the fixed point property for 1-dimensional continua, Fund. Math. 136 (1990), 27-36.
• [13] M. M. Marsh, Covering spaces, inverse limits, and induced coincidence producing mappings, Houston J. Math. 29 (2003), 983-992.
• [14] R. L. Russo, Universal continua, Fund. Math. 105 (1979), 41-60.
• [15] K. Sieklucki, On a class of plane acyclic continua with the fixed point property, Fund. Math. 63 (1968), 257-278.
• [16] A. L. Yandl, On a question concerning fixed points, Amer. Math. Monthly 75 (1968), 152-156.