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## Fundamenta Mathematicae

1994 | 144 | 1 | 1-9
Tytuł artykułu

### On spirals and fixed point property

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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.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
1-9
Opis fizyczny
Daty
wydano
1994
otrzymano
1991-04-08
poprawiono
1991-11-16
poprawiono
1992-12-03
Twórcy
autor
• 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.
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