Displaying similar documents to “Connected covers and Neisendorfer's localization theorem”

The geometry of laminations

Robbert Fokkink, Lex Oversteegen (1996)

Fundamenta Mathematicae

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A lamination is a continuum which locally is the product of a Cantor set and an arc. We investigate the topological structure and embedding properties of laminations. We prove that a nondegenerate lamination cannot be tree-like and that a planar lamination has at least four complementary domains. Furthermore, a lamination in the plane can be obtained by a lakes of Wada construction.

Analytic gaps

Stevo Todorčević (1996)

Fundamenta Mathematicae

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We investigate when two orthogonal families of sets of integers can be separated if one of them is analytic.

Period doubling, entropy, and renormalization

Jun Hu, Charles Tresser (1998)

Fundamenta Mathematicae

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We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point. Similar techniques then allow us to show that, under mild assumptions, smooth multimodal maps whose set of periods is the set of all powers of 2 are infinitely renormalizable with the diameters of all periodic intervals going to zero as the period goes to infinity.

Dense orderings, partitions and weak forms of choice

Carlos González (1995)

Fundamenta Mathematicae

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We investigate the relative consistency and independence of statements which imply the existence of various kinds of dense orders, including dense linear orders. We study as well the relationship between these statements and others involving partition properties. Since we work in ZF (i.e. without the Axiom of Choice), we also analyze the role that some weaker forms of AC play in this context

The measure algebra does not always embed

Alan Dow, Klaas Hart (2000)

Fundamenta Mathematicae

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The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(ℕ)/fin. We also discuss errors in previous results on the embeddability of the measure algebra.

Gaps in analytic quotients

Stevo Todorčević (1998)

Fundamenta Mathematicae

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We prove that the quotient algebra P(ℕ)/I over any analytic ideal I on ℕ contains a Hausdorff gap.