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- W2076126465 abstract "A well-known theorem of R. L. Moore states that the plane does not contain an uncountable family of pairwise disjoint triods. In 1974, Ingram demonstrated that the same is not true for non-chainable tree-like continua. The continua in Ingram’s family are not pairwise homeomorphic, making the example less applicable to the study of homogeneous continua in the plane. In this paper, we construct a non-chainable tree-like continuum <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that the product of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper X> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=application/x-tex>X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with the Cantor set can be embedded in the plane." @default.
- W2076126465 created "2016-06-24" @default.
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- W2076126465 date "2013-03-04" @default.
- W2076126465 modified "2023-09-27" @default.
- W2076126465 title "An uncountable family of copies of a non-chainable tree-like continuum in the plane" @default.
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- W2076126465 doi "https://doi.org/10.1090/s0002-9939-2013-11760-0" @default.
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