  We recall a characterization of hereditary indecomposability originally
obtained by Krasinkiewicz and Minc, and show how it may be used to give unified
constructions of various hereditarily indecomposable continua. In particular we
answer a question asked by Mackowiak and Tymchatyn by showing that any
continuum of arbitrary weight is a weakly confluent image of a hereditarily
indecomposable continuum of the same weight.
  We present two methods of constructing these preimages: (a) by
model-theoretic means, using the compactness and completeness theorems from
first-order logic to derive these results for continua of uncountable weight
from their metric counterparts; and (b) by constructing essential mappings from
hereditarily indecomposable continua onto Tychonoff cubes.
  We finish by reviving an argument due to Kelley about hyperspaces of
hereditarily indecomposable continua and show how it leads to a point-set
argument that reduces Brouwer's Fixed-point theorem to its three-dimensional
version.

General Topology;Logic