Inverse limit spaces defined by only finitely many distinct bonding maps
R. Jolly, James Rogers (1970)
Fundamenta Mathematicae
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R. Jolly, James Rogers (1970)
Fundamenta Mathematicae
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Chris Good, Brian E. Raines (2006)
Fundamenta Mathematicae
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We demonstrate that the set of topologically distinct inverse limit spaces of tent maps with a Cantor set for its postcritical ω-limit set has cardinality of the continuum. The set of folding points (i.e. points at which the space is not homeomorphic to the product of a zero-dimensional set and an arc) of each of these spaces is also a Cantor set.
Dorothy S. Marsh (1980)
Colloquium Mathematicae
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James Davis, W. Ingram (1988)
Fundamenta Mathematicae
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H. Cook (1967)
Fundamenta Mathematicae
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David Ryden (2000)
Fundamenta Mathematicae
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A procedure for obtaining points of irreducibility for an inverse limit on intervals is developed. In connection with this, the following are included. A semiatriodic continuum is defined to be a continuum that contains no triod with interior. Characterizations of semiatriodic and unicoherent continua are given, as well as necessary and sufficient conditions for a subcontinuum of a semiatriodic and unicoherent continuum M to lie within the interior of a proper subcontinuum of M. ...
Lee Mohler, Lex Oversteegen (1990)
Fundamenta Mathematicae
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Lee Mohler, Lex Oversteegen (1984)
Fundamenta Mathematicae
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J. Krasinkiewicz, Sam Nadler (1978)
Fundamenta Mathematicae
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J. Grispolakis, E. Tymchatyn (1980)
Fundamenta Mathematicae
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K. Kawamura, E. Tymchatyn (1996)
Colloquium Mathematicae
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A symmetric, idempotent, continuous binary operation on a space is called a mean. In this paper, we provide a criterion for the non-existence of mean on a certain class of continua which includes tree-like continua. This generalizes a result of Bell and Watson. We also prove that any hereditarily indecomposable circle-like continuum admits no mean.