It is shown that a number of
important results concerning irreducible metric continua can be generalized to
(nonmetric) irreducible continua. For example, if M is a (nonmetric) continuum
which is irreducible between a pair of points and which contains no indecomposable
subcontinuum with interior, then there exists a monotone continuous map of
M onto a generalized arc, such that each point inverse has void interior.
This result is applied to a study of hereditarily unicoherent, hereditarily
decomposable continua. Certain properties of trees follow as corollaries.
Also, trees are characterized as inverse limits of monotone inverse systems of
dendrites.
