Fibered products of homogeneous continua

Villarreal, Karen

doi:10.1090/S0002-9947-1993-1176510-X

Fibered products of homogeneous continua
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by Karen Villarreal PDF

Trans. Amer. Math. Soc. 338 (1993), 933-939 Request permission

Abstract:

In this paper, we construct homogeneous continua by using a fibered product of a homogeneous continuum $X$ with itself. The space $X$ must have a continuous decomposition into continua, and it must possess a certain type of homogeneity property with respect to this decomposition. It is known that the points of any one-dimensional, homogeneous continuum can be "blown up" into pseudo-arcs to form a new continuum with a continuous decomposition into pseudo-arcs. We will show that these continua can be used in the above construction. Finally, we will show that the continuum constructed by using the pseudo-arcs, the circle of pseudo-arcs, or the solenoid of pseudo-arcs is not homeomorphic to any known homogeneous continuum.

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Un continua dont tout sous-continu est indecomposable

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