Embeddings of the pseudo-arc in E²

Wayne Steven Lewis

Vol. 93 (1981), No. 1, 115–120

DOI: 10.2140/pjm.1981.93.115

Abstract

In this paper, we show that there exists an embedding, P_s, of the pseudo-arc in the plane such that any two accessible points lie in distinct composants of P_s. We also show that there are c = 2^ω₀ distinct embeddings of the pseudo-arc in the plane, including for each positive integer n, one with exactly n composants accessible. This answers some questions and a conjecture of Brechner.

Mathematical Subject Classification 2000

Primary: 54F20, 54F20

Secondary: 57N35

Milestones

Received: 24 October 1977

Revised: 17 December 1979

Published: 1 March 1981