On spirals and fixed point property

• Autorzy: Roman Mańka
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54F50: Spaces of dimension ≤ 1 ; curves, dendrites
• 54H25: Fixed-point and coincidence theorems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1994
• Tom: 144
• Numer: 1
• Strony: 1-9

Daty

wydano

1994

otrzymano

1991-04-08

poprawiono

1991-11-16

poprawiono

1992-12-03

Twórcy

autor

Roman Mańka

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-950 Warszawa, Poland

Bibliografia

• [1] M. M. Awartani, The fixed remainder property for self-homeomorphisms of Elsa continua, Topology Proc. 11 (1986), 225-238.
• [2] R. H. Bing, The elusive fixed point property, Amer. Math. Monthly 76 (1969), 119-132.
• [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.
• [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.
• [7] G. S. Young, Fixed-point theorems for arcwise connected continua, Proc. Amer. Math. Soc. 11 (1960), 880-884.