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 can be embedded in ” is consistent with MA + ¬ wKH.
Zoran Spasojević (1995)
Fundamenta Mathematicae
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I prove that the statement that “every linear order of size can be embedded in ” is consistent with MA + ¬ wKH.
Marcel Bökstedt, Iver Ottosen (1999)
Fundamenta Mathematicae
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Let X be a space with free loop space ΛX and mod two cohomology R = H*X. We construct functors and ℓ(R) together with algebra homomorphisms and . When X is 1-connected and R is a symmetric algebra we show that these are isomorphisms.
Peter Saveliev (1999)
Fundamenta Mathematicae
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A Lefschetz-type coincidence theorem for two maps f,g: X → Y from an arbitrary topological space to a manifold is given: , that is, the coincidence index is equal to the Lefschetz number. It follows that if then there is an x ∈ X such that f(x) = g(x). In particular, the theorem contains well-known coincidence results for (i) X,Y manifolds, f boundary-preserving, and (ii) Y Euclidean, f with acyclic fibres. It also implies certain fixed point results for multivalued maps with “point-like”...
Gary Gruenhage, J. Moore (2000)
Fundamenta Mathematicae
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A space X is called an α-Toronto space if X is scattered of Cantor-Bendixson rank α and is homeomorphic to each of its subspaces of the same rank. We answer a question of Steprāns by constructing a countable α-Toronto space for each α ≤ ω. We also construct consistent examples of countable α-Toronto spaces for each .
Krzysztof Barański (1998)
Fundamenta Mathematicae
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This is the first part of the work studying the family of all rational maps of degree three with two superattracting fixed points. We determine the topological type of the moduli space of and give a detailed study of the subfamily consisting of maps with a critical point which is periodic of period 2. In particular, we describe a parabolic bifurcation in from Newton maps to maps with so-called exotic basins.
A. Rotkiewicz (1999)
Acta Arithmetica
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Stéphane Louboutin, Young-Ho Park, Yann Lefeuvre (1999)
Acta Arithmetica
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R. Grant Woods (1995)
Fundamenta Mathematicae
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It is shown that associated with each metric space (X,d) there is a compactification of X that can be characterized as the smallest compactification of X to which each bounded uniformly continuous real-valued continuous function with domain X can be extended. Other characterizations of are presented, and a detailed study of the structure of is undertaken. This culminates in a topological characterization of the outgrowth , where is Euclidean n-space with its usual metric. ...
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 , 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.
Davide Ferrario (1998)
Fundamenta Mathematicae
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In order to compute the Nielsen number N(f) of a self-map f: X → X, some Reidemeister classes in the fundamental group need to be distinguished. In this paper some algebraic results are given which allow distinguishing Reidemeister classes and hence computing the Reidemeister number of some maps. Examples of computations are presented.
Gary Gruenhage, Yasunao Hattori, Haruto Ohta (1998)
Fundamenta Mathematicae
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For a subspace A of a space X, a linear extender φ:C(A) → C(X) is called an -extender (resp. -extender) if φ(f)[X] is included in the convex hull (resp. closed convex hull) of f[A] for each f ∈ C(A). Consider the following conditions (i)-(vii) for a closed subset A of a GO-space X: (i) A is a retract of X; (ii) A is a retract of the union of A and all clopen convex components of X; (iii) there is a continuous -extender φ:C(A × Y) → C(X × Y), with respect to both the compact-open topology...
Saharon Shelah, Oren Kolman (1996)
Fundamenta Mathematicae
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We assume a theory T in the logic is categorical in a cardinal λ κ, and κ is a measurable cardinal. We prove that the class of models of T of cardinality < λ (but ≥ |T|+κ) has the amalgamation property; this is a step toward understanding the character of such classes of models.
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 -complete and that the set of Cauchy problems which locally have a unique solution is -complete. We prove that the set of Cauchy problems which have a global solution is...
Bernd Günther, L. Mdzinarishvili (1997)
Fundamenta Mathematicae
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We prove that Alexander-Spanier cohomology with coefficients in a topologicalAbelian group G is isomorphic to the group of isomorphism classes of principal bundles with certain Abelian structure groups. The result holds if either X is a CW-space and G arbitrary or if X is metrizable or compact Hausdorff and G an ANR.
Valentin Gutev, Haruto Ohta (2000)
Fundamenta Mathematicae
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The above question was raised by Teodor Przymusiński in May, 1983, in an unpublished manuscript of his. Later on, it was recognized by Takao Hoshina as a question that is of fundamental importance in the theory of rectangular normality. The present paper provides a complete affirmative solution. The technique developed for the purpose allows one to answer also another question of Przymusiński's.