Non-additivity of the fixed point property for tree-like continua

• Autorzy: C. L. Hagopian , M. M. Marsh
• Języki publikacji: EN

Abstrakty

EN

We investigate the fixed point property for tree-like continua that are unions of tree-like continua. We obtain a positive result if finitely many tree-like continua with the fixed point property have dendrites for pairwise intersections. Using Bellamy's seminal example, we define (i) a countable wedge X̂ of tree-like continua, each having the fpp, and X̂ admitting a fixed-point-free homeomorphism, and (ii) two tree-like continua H and K such that H, K, and H∩ K have the fixed point property, but H ∪ K admits a fixed-point-free homeomorphism. In an appendix we verify some of the properties of Bellamy's continuum.

Kategorie tematyczne

• 54F15: Continua and generalizations
• 54G20: Counterexamples
• 54H25: Fixed-point and coincidence theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2015
• Tom: 231
• Numer: 2
• Strony: 113-137

Daty

wydano

2015

Twórcy

autor

C. L. Hagopian

• Department of Mathematics & Statistics, California State University, Sacramento, Sacramento, CA 95819-6051, U.S.A.

autor

M. M. Marsh

• Department of Mathematics & Statistics, California State University, Sacramento, Sacramento, CA 95819-6051, U.S.A.

Identyfikatory

DOI

10.4064/fm231-2-2