On spirals and fixed point property
Volume 144 / 1994
Fundamenta Mathematicae 144 (1994), 1-9 DOI: 10.4064/fm-144-1-1-9
We study the famous examples of G. S. Young  and R. H. Bing . 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.