Arcwise Connectedness of Semiaposyndetic Plane Continua

Abstract

In a recent paper, the author proved that if a compact plane continuum $M$ contains a finite point set $F$ such that, for each point $x$ in $M - F,M$ is semi-locally-connected and not aposyndetic at $x$, then $M$ 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.