Currently displaying 1 – 2 of 2

Showing per page

Order by Relevance | Title | Year of publication

Set-theoretic constructions of two-point sets

Ben Chad;  Robin Knight;  Rolf Suabedissen — 2009

Fundamenta Mathematicae

A two-point set is a subset of the plane which meets every line in exactly two points. By working in models of set theory other than ZFC, we demonstrate two new constructions of two-point sets. Our first construction shows that in ZFC + CH there exist two-point sets which are contained within the union of a countable collection of concentric circles. Our second construction shows that in certain models of ZF, we can show the existence of two-point sets without explicitly invoking the Axiom of Choice....

Uncountable ω-limit sets with isolated points

Chris Good;  Brian E. Raines;  Rolf Suabedissen — 2009

Fundamenta Mathematicae

We give two examples of tent maps with uncountable (as it happens, post-critical) ω-limit sets, which have isolated points, with interesting structures. Such ω-limit sets must be of the form C ∪ R, where C is a Cantor set and R is a scattered set. Firstly, it is known that there is a restriction on the topological structure of countable ω-limit sets for finite-to-one maps satisfying at least some weak form of expansivity. We show that this restriction does not hold if the ω-limit set is uncountable....

Page 1

Download Results (CSV)