A property equivalent to being semi-Kelley

TL;DR

This paper introduces a new property equivalent to being semi-Kelley, explores its hereditary nature in atriodic continua, and distinguishes semi-Kelley remainders from Kelley remainders with specific examples and properties.

Contribution

It establishes an equivalence characterization of semi-Kelley and investigates its hereditary and remaindering properties in various continua.

Findings

Semi-Kelley is hereditary for atriodic continua.

Semi-Kelley remainders are atriodic.

An example distinguishes semi-Kelley remainders from Kelley remainders.

Abstract

We present a property equivalent to the property of being semi-Kelley. Using this equivalence we prove that being semi-Kelley is a hereditary property for atriodic continua. We prove that semi-Kelley remainders are atriodic, moreover, we prove that semi-Kelley continua are semi-Kelley remainders for chainable continua, circularly chainable continua, and arc continua, and we give an example of an atriodic Kelley continuum which is a semi-Kelley remainder and not a Kelley remainder. We also prove that hereditarily semi-Kelley dendroids are smooth.