The Non-existence of Common Models for Certain Classes of Continua

Abstract In this paper, we first prove that for each continuum $$ Z $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Z</mml:mi> </mml:math> , the class of all hereditarily indecomposable continua $$ Y_Z $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Y</mml:mi> <mml:mi>Z</mml:mi> </mml:msub> </mml:math> that map onto $$ Z $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Z</mml:mi> </mml:math> by a light map does not admit a common model. Also, for several topological properties previously shown not to be Whitney reversible, we demonstrate that the corresponding classes of continua forming the counterexamples do not admit a common model.