Outlet points and homogeneous continua

Krupski, Paweł; Prajs, Janusz R.

doi:10.1090/S0002-9947-1990-0937246-8

Outlet points and homogeneous continua
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by Paweł Krupski and Janusz R. Prajs PDF

Trans. Amer. Math. Soc. 318 (1990), 123-141 Request permission

Abstract:

(1) A proof is presented for Bing’s conjecture that homogeneous, treelike continua are hereditarily indecomposable. As a consequence, each homogeneous curve admits the continuous decomposition into the maximal terminal, homeomorphic, homogeneous, hereditarily indecomposable, treelike subcontinua. (2) A homogeneous, hereditarily unicoherent continuum contains either an arc or arbitrarily small, nondegenerate, indecomposable subcontinua. (3) A treelike continuum with property $K$ which is homogeneous with respect to confluent light mappings contains no two nondegenerate subcontinua with the one-point intersection.

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