Homology cylinders and the acyclic closure of a free group.
Sakasai, Takuya (2006)
Algebraic & Geometric Topology
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Sakasai, Takuya (2006)
Algebraic & Geometric Topology
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Hutchings, Michael, Sullivan, Michael (2006)
Geometry & Topology
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Vo-Thanh Liem, Gerard Venema (1995)
Fundamenta Mathematicae
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Knot complements in the n-sphere are characterized. A connected open subset W of is homeomorphic with the complement of a locally flat (n-2)-sphere in , n ≥ 4, if and only if the first homology group of W is infinite cyclic, W has one end, and the homotopy groups of the end of W are isomorphic to those of in dimensions less than n/2. This result generalizes earlier theorems of Daverman, Liem, and Liem and Venema.
Paul Erdös, Steve Jackson, R. Mauldin (1994)
Fundamenta Mathematicae
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We consider a set, L, of lines in and a partition of L into some number of sets: . We seek a corresponding partition such that each line l in meets the set in a set whose cardinality has some fixed bound, . We determine equivalences between the bounds on the size of the continuum, , and some relationships between p, and .
Krzysztof Barański (1995)
Fundamenta Mathematicae
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We study the Julia sets for some periodic meromorphic maps, namely the maps of the form where h is a rational function or, equivalently, the maps . When the closure of the forward orbits of all critical and asymptotic values is disjoint from the Julia set, then it is hyperbolic and it is possible to construct the Gibbs states on J(˜f) for -α log |˜˜f|. For ˜α = HD(J(˜f)) this state is equivalent to the ˜α-Hausdorff measure or to the ˜α-packing measure provided ˜α is greater or smaller...
Joan Hart, Kenneth Kunen (1996)
Fundamenta Mathematicae
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Let X be a compact Hausdorff space and M a metric space. is the set of f ∈ C(X,M) such that there is a dense set of points x ∈ X with f constant on some neighborhood of x. We describe some general classes of X for which is all of C(X,M). These include βℕ, any nowhere separable LOTS, and any X such that forcing with the open subsets of X does not add reals. In the case where M is a Banach space, we discuss the properties of as a normed linear space. We also build three first countable...
John Cobb (1994)
Fundamenta Mathematicae
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As a special case of the general question - “What information can be obtained about the dimension of a subset of by looking at its orthogonal projections into hyperplanes?” - we construct a Cantor set in each of whose projections into 2-planes is 1-dimensional. We also consider projections of Cantor sets in whose images contain open sets, expanding on a result of Borsuk.
V. Shavrukov (1997)
Fundamenta Mathematicae
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For finitely axiomatized sequential theories F and reflexive theories R, we give a characterization of the relation ’F interprets R’ in terms of provability of restricted consistency statements on cuts. This characterization is used in a proof that the set of (as well as ) sentences π such that GB interprets ZF+π is -complete.
Péter Komjáth (1998)
Fundamenta Mathematicae
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It is consistent that but .
Gabriel Debs, Jean Saint Raymond (1999)
Fundamenta Mathematicae
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We study properties of and subsets of that are cofinal relative to the orders ≤ (≤*) of full (eventual) domination. We apply these results to prove that the topological statement “Any compact covering mapping from a Borel space onto a Polish space is inductively perfect” is equivalent to the statement " is bounded for ≤*".
M. Kühleitner, W. G. Nowak, J. Schoissengeier, T. D. Wooley (1998)
Acta Arithmetica
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The arithmetic function counts the number of ways to write a natural number n as a sum of two kth powers (k ≥ 2 fixed). The investigation of the asymptotic behaviour of the Dirichlet summatory function of leads in a natural way to a certain error term which is known to be in mean-square. In this article it is proved that as t → ∞. Furthermore, it is shown that a similar result would be true for every fixed k > 3 provided that a certain set of algebraic numbers contains a...
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. ...
Tamás Keleti (1998)
Fundamenta Mathematicae
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We investigate some problems of the following type: For which sets H is it true that if f is in a given class ℱ of periodic functions and the difference functions are in a given smaller class G for every h ∈ H then f itself must be in G? Denoting the class of counter-example sets by ℌ(ℱ,G), that is, , we try to characterize ℌ(ℱ,G) for some interesting classes of functions ℱ ⊃ G. We study classes of measurable functions on the circle group that are invariant for changes on null-sets...
Friedrich Bauer (1997)
Fundamenta Mathematicae
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In the S-category (with compact-open strong shape mappings, cf. §1, instead of continuous mappings, and arbitrary finite-dimensional separable metrizable spaces instead of finite polyhedra) there exists according to [1], [2] an S-duality. The S-dual , turns out to be of the same weak homotopy type as an appropriately defined functional dual (Corollary 4.9). Sometimes the functional object is of the same weak homotopy type as the “real” function space (§5).
José Iovino (1998)
Fundamenta Mathematicae
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We prove a geometric characterization of Banach space stability. We show that a Banach space X is stable if and only if the following condition holds. Whenever is an ultrapower of X and B is a ball in , the intersection B ∩ X can be uniformly approximated by finite unions and intersections of balls in X; furthermore, the radius of these balls can be taken arbitrarily close to the radius of B, and the norm of their centers arbitrarily close to the norm of the center of B. The preceding...
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.
Gary Gruenhage, Piotr Koszmider (1996)
Fundamenta Mathematicae
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We show that MA implies that normal locally compact metacompact spaces are paracompact, and that MA() implies normal locally compact metalindelöf spaces are paracompact. The latter result answers a question of S. Watson. The first result implies that there is a model of set theory in which all normal locally compact metacompact spaces are paracompact, yet there is a normal locally compact metalindelöf space which is not paracompact.