chapter  Chapter 5
62 Pages

Decomposition Theorems

WithSergio Macías

We present a proof of Jones’s Aposyndetic Decomposition Theorem and Rogers’s Terminal Decomposition Theorem. These theorems are proven using Jones’s set function 𝒯 (Chapter 3) and Effros’s Theorem (Chapter 4). We also give a construction of the Case continuum and present a sketch of the construction of the Minc– Rogers continua. Finally, we study covering spaces of any solenoid, the Menger curve, the Case continuum and one of the Minc–Rogers examples.