On <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math>-homogeneous continua

Neumann-Lara, Víctor; Pellicer-Covarrubias, Patricia; Puga, Isabel

doi:10.1016/j.topol.2005.10.005

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Cited by 19 publications

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$$1/\kappa $$ 1 / κ -Homogeneous long solenoids

2016

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We study nonmetric analogues of Vietoris solenoids. Let be an ordered continuum, and let p = p 1 , p 2 , . . . be a sequence of positive integers. We define a natural inverse limit space S( , p), where the first factor space is the nonmetric "circle" obtained by identifying the endpoints of , and the nth factor space, n > 1, consists of p 1 p 2 . . . p n−1 copies of laid end to end in a circle. We prove that for every cardinal κ ≥ 1, there is an ordered continuum such that S( , p) is relation similar to one used to classify the additive subgroups of Q. Consequently, for each fixed , as p varies, there are exactly c-many different shapes, where c = 2 ℵ 0 , (and there are also exactly that many homeomorphism types) represented by S( , p).

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