1Department of Mathematics California State University, Sacramento Sacramento, CA 95819-6051, U.S.A. 2Department of Mathematics California State University, Sacramento Sacramento, CA 95819-6051, U.S.A. and Institute of Mathematics and Informatics Opole University Oleska 48, Opole, Poland
Fundamenta Mathematicae, Tome 186 (2005) no. 3, pp. 233-249
We define an unusual continuum $M$
with the fixed-point property in the plane $\mathbb R^2$. There is a disk $D$ in $\mathbb R^2$ such that $M \cap D$
is an arc and $M \cup D$ does not have the fixed-point property. This example answers
a question of R. H. Bing. The continuum $M$ is a countable union of arcs.
Keywords:
define unusual continuum fixed point property plane mathbb there disk mathbb cap arc cup does have fixed point property example answers question bing continuum countable union arcs
Affiliations des auteurs :
Charles L. Hagopian
1
;
Janusz R. Prajs
2
1
Department of Mathematics California State University, Sacramento Sacramento, CA 95819-6051, U.S.A.
2
Department of Mathematics California State University, Sacramento Sacramento, CA 95819-6051, U.S.A. and Institute of Mathematics and Informatics Opole University Oleska 48, Opole, Poland
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Charles L. Hagopian; Janusz R. Prajs. A fixed-point anomaly in the plane. Fundamenta Mathematicae, Tome 186 (2005) no. 3, pp. 233-249. doi: 10.4064/fm186-3-3
