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arXiv · 1608.00292

Widely-connected sets in the bucket-handle continuum

David Sumner Lipham
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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 Erd\H{o}s and Howard Cook, while a similar example answers a question of Jerzy Mioduszewski.

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David Sumner Lipham. 2016-08-01. Widely-connected sets in the bucket-handle continuum. https://doi.org/10.4064/fm378-3-2017

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