Displaying similar documents to “Classical-type characterizations of non-metrizable ANE(n)-spaces”

Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy problems in one dimension

Alessandro Andretta, Alberto Marcone (1997)

Fundamenta Mathematicae

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We study some natural sets arising in the theory of ordinary differential equations in one variable from the point of view of descriptive set theory and in particular classify them within the Borel hierarchy. We prove that the set of Cauchy problems for ordinary differential equations which have a unique solution is ∏ 2 0 -complete and that the set of Cauchy problems which locally have a unique solution is ∑ 3 0 -complete. We prove that the set of Cauchy problems which have a global solution is...

The Arkhangel’skiĭ–Tall problem: a consistent counterexample

Gary Gruenhage, Piotr Koszmider (1996)

Fundamenta Mathematicae

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We construct a consistent example of a normal locally compact metacompact space which is not paracompact, answering a question of A. V. Arkhangel’skiĭ and F. Tall. An interplay between a tower in P(ω)/Fin, an almost disjoint family in [ ω ] ω , and a version of an (ω,1)-morass forms the core of the proof. A part of the poset which forces the counterexample can be considered a modification of a poset due to Judah and Shelah for obtaining a Q-set by a countable support iteration.

Linear orders and MA + ¬wKH

Zoran Spasojević (1995)

Fundamenta Mathematicae

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I prove that the statement that “every linear order of size 2 ω can be embedded in ( ω ω , ≪ ) ” is consistent with MA + ¬ wKH.

From Newton’s method to exotic basins Part I: The parameter space

Krzysztof Barański (1998)

Fundamenta Mathematicae

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This is the first part of the work studying the family 𝔉 of all rational maps of degree three with two superattracting fixed points. We determine the topological type of the moduli space of 𝔉 and give a detailed study of the subfamily ℱ 2 consisting of maps with a critical point which is periodic of period 2. In particular, we describe a parabolic bifurcation in ℱ 2 from Newton maps to maps with so-called exotic basins.

Solution of the 1 : −2 resonant center problem in the quadratic case

Alexandra Fronville, Anton Sadovski, Henryk Żołądek (1998)

Fundamenta Mathematicae

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The 1:-2 resonant center problem in the quadratic case is to find necessary and sufficient conditions (on the coefficients) for the existence of a local analytic first integral for the vector field ( x + A 1 x 2 + B 1 x y + C y 2 ) ∂ x + ( - 2 y + D x 2 + A 2 x y + B 2 y 2 ) ∂ y . There are twenty cases of center. Their necessity was proved in [4] using factorization of polynomials with integer coefficients modulo prime numbers. Here we show that, in each of the twenty cases found in [4], there is an analytic first integral. We develop a new method of investigation...

Postnikov invariants of H-spaces

Dominique Arlettaz, Nicole Pointet-Tischler (1999)

Fundamenta Mathematicae

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It is known that the order of all Postnikov k-invariants of an H-space of finite type is finite. This paper establishes the finiteness of the order of the k-invariants k m + 1 ( X ) of X in dimensions m ≤ 2n if X is an (n-1)-connected H-space which is not necessarily of finite type (n ≥ 1). Similar results hold more generally for higher k-invariants if X is an iterated loop space. Moreover, we provide in all cases explicit universal upper bounds for the order of the k-invariants of X.

Hausdorff ’s theorem for posets that satisfy the finite antichain property

Uri Abraham, Robert Bonnet (1999)

Fundamenta Mathematicae

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Hausdorff characterized the class of scattered linear orderings as the least family of linear orderings that includes the ordinals and is closed under ordinal summations and inversions. We formulate and prove a corresponding characterization of the class of scattered partial orderings that satisfy the finite antichain condition (FAC).  Consider the least class of partial orderings containing the class of well-founded orderings that satisfy the FAC and is closed under the following operations:...

The structure of atoms (hereditarily indecomposable continua)

R. Ball, J. Hagler, Yaki Sternfeld (1998)

Fundamenta Mathematicae

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Let X be an atom (= hereditarily indecomposable continuum). Define a metric ϱ on X by letting ϱ ( x , y ) = W ( A x y ) where A x , y is the (unique) minimal subcontinuum of X which contains x and y and W is a Whitney map on the set of subcontinua of X with W(X) = 1. We prove that ϱ is an ultrametric and the topology of (X,ϱ) is stronger than the original topology of X. The ϱ-closed balls C(x,r) = y ∈ X:ϱ ( x,y) ≤ r coincide with the subcontinua of X. (C(x,r) is the unique subcontinuum of X which contains x and has...