On disconnected images of connected spaces
  We introduce the notion that a zero-dimensional compact space $L$ is a \emph{Boolean image} of an arbitrary compact space $K$. When $K$ is also zero-dimensional, this just means that $L$ is a continuous image of $K$. However, a number of interesting questions arise when we consider connected compacta $K$. 
Antonio Avil\'es, Grzegorz Plebanek
math.GN math.LO