Connection between set theory and the fixed point property
Fixed point theorems for λ-dendroids
On irreducibility and indecomposability of continua
On the additivity of the fixed point property for 1-dimensional continua
On spirals and fixed point property
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...
Association and fixed points
On fixed point theorems for multifunctions in dendroids
On uniquely arcwise connected curves
The topological fixed point property - an elementary continuum-theoretic approach
A set contained in a topological space has the topological fixed point property if every continuous mapping of the set into itself leaves some point fixed. In 1969, R. H. Bing published his article The Elusive Fixed Point Property, posing twelve intriguing and difficult problems, which exerted a great influence on the study of the fixed point property. We now present a survey article intended for a broad audience that reports on this area of fixed point theory. The exposition is also intended to...
The fixed point property for some cartesian products
It is proved that the cylinder X × I over a planar λ-dendroid X has the fixed point property. This is a partial solution of two problems posed by R. H. Bing (cf. [1], Questions 9 and 10).
Cylinders over λ-dendroids have the fixed point property
It is proved that the cylinder X × I over a λ-dendroid X has the fixed point property. The proof uses results of [9] and [10].
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