Menger curves in Peano continua
نویسندگان
چکیده
منابع مشابه
Hyperspaces of Peano continua of euclidean spaces
If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space L(R) is homeomorphic to B∞, where B denotes the pseudo-boundary of the Hilbert cube Q. Introduction. For a space X, C(X) denotes the hyperspace of all nonempty subcontinua of X. It is known that for a Peano continuum X without free arcs, C(X) ≈ Q, where Q denotes the H...
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It is shown that the homeomorphism groups of the (generalized) Sierpiński carpet and the universal Menger continua are not zero-dimensional. These results were corollaries to a 1966 theorem of Brechner. New proofs were needed because we also show that Brechner’s proof is inadequate. The method by which we obtain our results, the construction of closed imbeddings of complete Erdős space in the h...
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Our main theorem is that, if M is a closed hyperbolic 3–manifold which fibres over the circle with hyperbolic fibre S and pseudo-Anosov monodromy, then the lift of the inclusion of S in M to universal covers extends to a continuous map of B to B , where B D H [ S 1 1 . The restriction to S 1 maps onto S 1 and gives an example of an equivariant S –filling Peano curve. After proving the main theo...
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We construct Peano curves γ : r0,8q Ñ R2 whose “footprints” γpr0, tsq, t ą 0, have C8 boundaries and are tangent to a common continuous line field on the punctured plane R2 r tγp0qu. Moreover, these boundaries can be taken C8-close to any prescribed smooth family of nested smooth Jordan curves contracting to a point.
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We consider Thurston maps, i.e., branched covering maps f : S → S that are postcritically finite. It is shown that a Thurston map f is expanding (in a suitable sense) if and only if some iterate F = f is semi-conjugate to z : S → S, where d = deg F . More precisely, for such an F we construct a Peano curve γ : S → S (onto), such that F ◦ γ(z) = γ(z) (for all z ∈ S).
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1996
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-70-1-79-86