Widely-connected sets in the bucket-handle continuum

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.

15 pages, 5 figures

References in corpus (1)

• Problems from Topology Proceedings

Cited by in corpus (3)

• On cohesive almost zero-dimensional spaces
• On indecomposability of $\beta X$
• Embedding irreducible connected sets