Continua in which only semi-aposyndetic subcontinua separate

Leland Edward Rogers

Vol. 43 (1972), No. 2, 493–502

DOI: 10.2140/pjm.1972.43.493

Abstract

E. J. Vought has characterized hereditarily locally connected compact metric continua as those which are hereditarily aposyndetic, and (subsequently) as those which are aposyndetic and have only aposyndetic separating subcontinua. Also, Vought characterized hereditarily locally connected, cyclically connected compact metric continua as those having no cut point and separated only by aposyndetic subcontinua. In this paper it is shown that similar characterizatious can be obtained when a larger class of subcontinua are allowed to separate, namely those which are semi-aposyndetic.

Mathematical Subject Classification

Primary: 54F20

Milestones

Received: 22 June 1971

Revised: 1 March 1972

Published: 1 November 1972