## Widely-connected sets in the bucket-handle continuum

### Volume 240 / 2018

Fundamenta Mathematicae 240 (2018), 161-174
MSC: 54D05, 54F15, 54F50, 54E50, 54G20.
DOI: 10.4064/fm378-3-2017
Published online: 4 August 2017

#### Abstract

A connected topological space is said to be widely-connected if each of its non-degenerate connected subsets is dense in the entire space. The object of this paper is the construction of widely-connected subsets of the plane. We give a completely metrizable example that answers a question of Paul Erdős and Howard Cook, while a similar example answers a question of Jerzy Mioduszewski.