# On spirals and fixed point property

Fundamenta Mathematicae (1994)

- Volume: 144, Issue: 1, page 1-9
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topMańka, Roman. "On spirals and fixed point property." Fundamenta Mathematicae 144.1 (1994): 1-9. <http://eudml.org/doc/212012>.

@article{Mańka1994,

abstract = {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.},

author = {Mańka, Roman},

journal = {Fundamenta Mathematicae},

keywords = {uniquely arcwise connected continuum; Young space; Bing space},

language = {eng},

number = {1},

pages = {1-9},

title = {On spirals and fixed point property},

url = {http://eudml.org/doc/212012},

volume = {144},

year = {1994},

}

TY - JOUR

AU - Mańka, Roman

TI - On spirals and fixed point property

JO - Fundamenta Mathematicae

PY - 1994

VL - 144

IS - 1

SP - 1

EP - 9

AB - 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.

LA - eng

KW - uniquely arcwise connected continuum; Young space; Bing space

UR - http://eudml.org/doc/212012

ER -

## References

top- [1] M. M. Awartani, The fixed remainder property for self-homeomorphisms of Elsa continua, Topology Proc. 11 (1986), 225-238. Zbl0641.54031
- [2] R. H. Bing, The elusive fixed point property, Amer. Math. Monthly 76 (1969), 119-132. Zbl0174.25902
- [3] R. Engelking, Dimension Theory, PWN, Warszawa, and North-Holland, Amsterdam, 1978.
- [4] W. Holsztyński, Fixed points of arcwise connected spaces, Fund. Math. 69 (1969), 289-312. Zbl0185.26802
- [5] K. Kuratowski, Topology, Vols. I and II, Academic Press, New York, and PWN-Polish Scientific Publishers, Warszawa, 1966 and 1968.
- [6] R. Mańka, On uniquely arcwise connected curves, Colloq. Math. 51 (1987), 227-238. Zbl0637.54029
- [7] G. S. Young, Fixed-point theorems for arcwise connected continua, Proc. Amer. Math. Soc. 11 (1960), 880-884. Zbl0102.37806

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.