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1994 | 144 | 1 | 1-9

Tytuł artykułu

On spirals and fixed point property

Autorzy

Treść / Zawartość

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.

Rocznik

Tom

144

Numer

1

Strony

1-9

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.

Identyfikator YADDA

bwmeta1.element.bwnjournal-article-fmv144i1p1bwm