Some theorems on decomposable continua

TL;DR

This paper presents new theorems on decomposable continua, exploring properties like Wilder continua and D**-continua, and establishing their relationships and non-reversibility under certain conditions.

Contribution

It introduces novel results on the properties and relationships of decomposable continua, including non-reversibility of Wilder continua and construction of specific D**-continua.

Findings

Wilder continuum property is not Whitney reversible.

Inverse limits of D**-continua with surjective monotone bonding functions are D**.

Existence of D**-continua without Wilder or D*-subcontinua.

Abstract

We prove some theorems on decomposable continua. In particular, we prove; (i) the property of being a Wilder continuum is not a Whitney reversible property, (ii) inverse limits of D**-continua with surjective monotone upper semi-continuous bonding functions are D**, and (iii) there exists a D**-continuum which contains neither Wilder continua nor D*-continua. Also, we show the existence of a Wilder continuum containing no D*-continua and a D*-continuum containing no Wilder continua.