Vol. 36, No. 3, 1971

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Monotone decompositions of irreducible Hausdorff continua

George Rudolph Gordh, Jr.

Vol. 36 (1971), No. 3, 647–658

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.

Mathematical Subject Classification
Primary: 54.55
Received: 10 September 1970
Published: 1 March 1971
George Rudolph Gordh, Jr.