Using brick partitionings to establish conditions which insure that a Peano continuum is a 2-cell, a 2-sphere or an annulus

Richard Alan Slocum

Vol. 42 (1972), No. 3, 763–775

DOI: 10.2140/pjm.1972.42.763

Abstract

Using brick patitioning, sufficient conditions are established for a subset of a Peano space to be locally euclidean. If M is a Peano space with no local cut points and S is a subcontinuum of M, has no local cut points, is the closure of a domain in M, has connected complement and contains a point x such that every simple closed curve in lS not passing through x separates M, then S is a closed 2-cell, a 2-sphere or an annulus.

Mathematical Subject Classification

Primary: 54F25

Milestones

Received: 21 September 1970

Revised: 2 June 1972

Published: 1 September 1972