Geodesic
Stable Homeomorphisms of the Pseudo-Arc
Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 363-374

Voir la notice de l'article provenant de la source Cambridge University Press

Noting that certain restrictions are placed on homeomorphisms of the pseudo-arc, since it is hereditarily indecomposable, in 1955 [4] R. H. Bing asked if the identity is the only stable homeomorphism of the pseudo-arc. In this paper we prove the following theorem.THEOREM. Let U be an open subset of the pseudo-arc P. Let p and q be distinct points of P such that the subcontinuum M irreducible between p and q does not intersect cl(U). Then there exists a homeomorphism h : P → P with h (p) = q andh│U = 1U. 1. Definitions. A chain C is a collection of open sets C = {C(i))}i≧n such that C(i) ∩ C(j) ≠ ∅ if and only if |i – j| ≦ 1, cl|(C(i)) ∩ cl(C(j)) ≠ ∅ if and only if |i – j| ≦ 1, C(0) – C(l) ≠ ∅, and C(n) – C(n – 1) ≠ ∅. Each C(i) is called a link of C. 
Lewis, Wayne. Stable Homeomorphisms of the Pseudo-Arc. Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 363-374. doi: 10.4153/CJM-1979-041-1
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