Displaying similar documents to “Analytic gaps”

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.

On a question of Sierpiński

Theodore Slaman (1999)

Fundamenta Mathematicae

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There is a set U of reals such that for every analytic set A there is a continuous function f which maps U bijectively to A.

Connected covers and Neisendorfer's localization theorem

C. McGibbon, J. Møller (1997)

Fundamenta Mathematicae

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Our point of departure is J. Neisendorfer's localization theorem which reveals a subtle connection between some simply connected finite complexes and their connected covers. We show that even though the connected covers do not forget that they came from a finite complex their homotopy-theoretic properties are drastically different from those of finite complexes. For instance, connected covers of finite complexes may have uncountable genus or nontrivial SNT sets, their Lusternik-Schnirelmann...

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.

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.

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 σ-ideal of closed smooth sets does not have the covering property

Carlos Uzcátegui (1996)

Fundamenta Mathematicae

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We prove that the σ-ideal I(E) (of closed smooth sets with respect to a non-smooth Borel equivalence relation E) does not have the covering property. In fact, the same holds for any σ-ideal containing the closed transversals with respect to an equivalence relation generated by a countable group of homeomorphisms. As a consequence we show that I(E) does not have a Borel basis.

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.

Borel extensions of Baire measures

J. Aldaz (1997)

Fundamenta Mathematicae

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We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space...