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.
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. ...
Valentin Gutev, Vesko Valov (1994)
Fundamenta Mathematicae
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The Kuratowski-Dugundji theorem that a metrizable space is an absolute (neighborhood) extensor in dimension n iff it is (resp., ) is extended to a class of non-metrizable absolute (neighborhood) extensors in dimension n. On this base, several facts concerning metrizable extensors are established for non-metrizable ones.
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.
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.
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:...
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...
Wojciech Olszewski (1994)
Fundamenta Mathematicae
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We construct a family of spaces with “nice” structure which is universal in the class of all compact metrizable spaces of large transfinite dimension , or, equivalently, of small transfinite dimension ; that is, the family consists of compact metrizable spaces whose transfinite dimension is , and every compact metrizable space with transfinite dimension is embeddable in a space of the family. We show that the least possible cardinality of such a universal family is equal to the...
James Schmerl (1999)
Fundamenta Mathematicae
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The following theorem is proved, answering a question raised by Davies in 1963. If is a partition of the set of lines of , then there is a partition such that whenever . There are generalizations to some other, higher-dimensional subspaces, improving recent results of Erdős, Jackson Mauldin.
Kasper Andersen (1999)
Fundamenta Mathematicae
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Let X be a p-compact group, with maximal torus BT → BX, maximal torus normalizer BN and Weyl group . We prove that for an odd prime p, the fibration has a section, which is unique up to vertical homotopy.
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”...
Dietrich Notbohm (1998)
Fundamenta Mathematicae
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We are interested in a topological realization of a family of pseudoreflection groups ; i.e. we are looking for topological spaces whose mod-p cohomology is isomorphic to the ring of invariants . Spaces of this type give partial answers to a problem of Steenrod, namely which polynomial algebras over can appear as the mod-p cohomology of a space. The family under consideration is given by pseudoreflection groups which are subgroups of the wreath product where q divides p - 1 and...
Tadeusz Dobrowolski, Leonard Rubin (1994)
Fundamenta Mathematicae
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The hyperspaces and in consisting respectively of all compact absolute neighborhood retracts and all compact absolute retracts are studied. It is shown that both have the Borel type of absolute -spaces and that, indeed, they are not -spaces. The main result is that is an absorber for the class of all absolute -spaces and is therefore homeomorphic to the standard model space of this class.
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 . 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...
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.
Paul Fabel (1998)
Fundamenta Mathematicae
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We prove that the space of orientation preserving homeomorphisms of the 2-sphere which fix pointwise a nontrivial nonseparating continuum is a contractible absolute neighborhood retract homeomorphic to the separable Hilbert space .
Harold Bennett, David Lutzer (1997)
Fundamenta Mathematicae
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For a space X and a regular uncountable cardinal κ ≤ |X| we say that κ ∈ D(X) if for each with |T| = κ, there is an open neighborhood W of Δ(X) such that |T - W| = κ. If then we say that X has a small diagonal, and if every regular uncountable κ ≤ |X| belongs to D(X) then we say that X has an H-diagonal. In this paper we investigate the interplay between D(X) and topological properties of X in the category of generalized ordered spaces. We obtain cardinal invariant theorems and metrization...
Wojciech Olszewski (1994)
Fundamenta Mathematicae
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For every countable non-limit ordinal α we construct an α-dimensional Cantor ind-manifold, i.e., a compact metrizable space such that , and no closed subset L of with ind L less than the predecessor of α is a partition in . An α-dimensional Cantor Ind-manifold can be constructed similarly.