We define an unusual continuum M with the fixed-point property in the plane ℝ². There is a disk D in ℝ² such that M ∩ D is an arc and M ∪ 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-3-3,
author = {Charles L. Hagopian and Janusz R. Prajs},
title = {A fixed-point anomaly in the plane},
journal = {Fundamenta Mathematicae},
volume = {185},
year = {2005},
pages = {233-249},
zbl = {1101.54036},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-3-3}
}
Charles L. Hagopian; Janusz R. Prajs. A fixed-point anomaly in the plane. Fundamenta Mathematicae, Tome 185 (2005) pp. 233-249. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm186-3-3/