Continuum theory (Q2874867)

The paper concerns the metric continua on the plane. The authors discuss the current research of three problems, hence it consists of three sections. In the first section ``Homogeneous continua in the plane'' the authors discuss the problem of classifying all homogeneous continua in the plane. Note that the first author solved this problem in 2015: in the plane there are exactly three nondegenerate homogeneous continua -- the circle, the pseudoarc and the circle of pseudoarcs. In the second section ``The plane fixed point problem'' the following problem is discussed: if \(X\) is a plane continuum which does not disconnect the plane and if \(f : X \rightarrow X\) is a continuous function, does there exist \(x \in X\) such that \(f(x) = x\)? In the third section ``Lamination and complex dynamics'' the authors describe the connection between laminations and polynomials (acting on the complex plane) with locally connected Julia set.NEWLINENEWLINEFor the entire collection see [Zbl 1282.54001].