On spirals and fixed point property

Roman Mańka

Fundamenta Mathematicae (1994)

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

Abstract

top
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.

How to cite

top

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

NotesEmbed ?

top

You must be logged in to post comments.