Arcwise connectedness of semiaposyndetic plane continua

Abstract

In a recent paper, the author proved that if a compact plane continuum M M contains a finite point set F F such that, for each point x x in M − F , M M - F,M is semi-locally-connected and not aposyndetic at x x , then M M is arcwise connected. The primary purpose of this paper is to generalize that theorem. Semiaposyndesis, a generalization of semi-local-connectedness, is defined and arcwise connectedness is established for certain semiaposyndetic plane continua.