We study the famous examples of G. S. Young [7] and R. H. Bing [2]. We generalize and simplify a little their constructions. First we introduce Young spirals which play a basic role in all considerations. We give a construction of a Young spiral which does not have the fixed point property (see Section 5) . Then, using Young spirals, we define two classes of uniquely arcwise connected curves, called Young spaces and Bing spaces. These classes are analogous to the examples mentioned above. The definitions identify the basic distinction between these classes. The main results are Theorems 4.1 and 6.1.
@article{bwmeta1.element.bwnjournal-article-fmv144i1p1bwm,
author = {Roman Ma\'nka},
title = {On spirals and fixed point property},
journal = {Fundamenta Mathematicae},
volume = {144},
year = {1994},
pages = {1-9},
zbl = {0809.54030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv144i1p1bwm}
}
Mańka, Roman. On spirals and fixed point property. Fundamenta Mathematicae, Tome 144 (1994) pp. 1-9. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv144i1p1bwm/
[00000] [1] M. M. Awartani, The fixed remainder property for self-homeomorphisms of Elsa continua, Topology Proc. 11 (1986), 225-238. | Zbl 0641.54031
[00001] [2] R. H. Bing, The elusive fixed point property, Amer. Math. Monthly 76 (1969), 119-132. | Zbl 0174.25902
[00002] [3] R. Engelking, Dimension Theory, PWN, Warszawa, and North-Holland, Amsterdam, 1978.
[00003] [4] W. Holsztyński, Fixed points of arcwise connected spaces, Fund. Math. 69 (1969), 289-312. | Zbl 0185.26802
[00004] [5] K. Kuratowski, Topology, Vols. I and II, Academic Press, New York, and PWN-Polish Scientific Publishers, Warszawa, 1966 and 1968.
[00005] [6] R. Mańka, On uniquely arcwise connected curves, Colloq. Math. 51 (1987), 227-238. | Zbl 0637.54029
[00006] [7] G. S. Young, Fixed-point theorems for arcwise connected continua, Proc. Amer. Math. Soc. 11 (1960), 880-884. | Zbl 0102.37806