Vol. 23, No. 3, 1967

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Inverse limits of indecomposable continua

J. H. Reed

Vol. 23 (1967), No. 3, 597–600

Let {Xλ,fλμ,Λ} denote an inverse limit system of continua, with inverse limit space X. Capel has shown that if each Xλ is an arc (simple closed curve), then X is an arc (simple closed curve) provided that Λ is countable and the bonding maps are monotone and onto. It is shown in this paper that a similar result holds when each Xλ is a pseudoarc. In fact, the restrictions that the bonding maps be monotone and onto may be deleted.

Two theorems are proved which lead to this result. First, it is shown that if the maps of an inverse system of indecomposable continua are onto, then the limit space is an indecomposable continuum. Next, it is shown that with no restrictions on the bonding maps, a similar statement is true for hereditarily indecomposable continua.

Mathematical Subject Classification
Primary: 54.55
Received: 7 June 1966
Published: 1 December 1967
J. H. Reed