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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Fibered products of homogeneous continua


Author: Karen Villarreal
Journal: Trans. Amer. Math. Soc. 338 (1993), 933-939
MSC: Primary 54F15; Secondary 54G20
DOI: https://doi.org/10.1090/S0002-9947-1993-1176510-X
MathSciNet review: 1176510
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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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DOI: https://doi.org/10.1090/S0002-9947-1993-1176510-X
Keywords: Continuum, homogeneous, fibered product, aposyndetic continuum, continuous decomposition, pseudo-arc, circle of pseudo-arcs, solenoid of pseudo-arcs
Article copyright: © Copyright 1993 American Mathematical Society