Displaying similar documents to “Homology lens spaces and Dehn surgery on homology spheres”

Characterization of knot complements in the n-sphere

Vo-Thanh Liem, Gerard Venema (1995)

Fundamenta Mathematicae

Similarity:

Knot complements in the n-sphere are characterized. A connected open subset W of S n is homeomorphic with the complement of a locally flat (n-2)-sphere in S n , 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 S 1 in dimensions less than n/2. This result generalizes earlier theorems of Daverman, Liem, and Liem and Venema.

On partitions of lines and space

Paul Erdös, Steve Jackson, R. Mauldin (1994)

Fundamenta Mathematicae

Similarity:

We consider a set, L, of lines in n and a partition of L into some number of sets: L = L 1 . . . L p . We seek a corresponding partition n = S 1 . . . S p such that each line l in L i meets the set S i in a set whose cardinality has some fixed bound, ω τ . We determine equivalences between the bounds on the size of the continuum, 2 ω ω θ , and some relationships between p, ω τ and ω θ .

Hausdorff dimension and measures on Julia sets of some meromorphic maps

Krzysztof Barański (1995)

Fundamenta Mathematicae

Similarity:

We study the Julia sets for some periodic meromorphic maps, namely the maps of the form f ( z ) = h ( e x p 2 π i T z ) where h is a rational function or, equivalently, the maps ˜ f ( z ) = e x p ( 2 π i h ( z ) ) . 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...

Locally constant functions

Joan Hart, Kenneth Kunen (1996)

Fundamenta Mathematicae

Similarity:

Let X be a compact Hausdorff space and M a metric space. E 0 ( X , M ) 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 E 0 ( X , M ) 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 E 0 ( X , M ) as a normed linear space. We also build three first countable...

Raising dimension under all projections

John Cobb (1994)

Fundamenta Mathematicae

Similarity:

As a special case of the general question - “What information can be obtained about the dimension of a subset of n by looking at its orthogonal projections into hyperplanes?” - we construct a Cantor set in 3 each of whose projections into 2-planes is 1-dimensional. We also consider projections of Cantor sets in n whose images contain open sets, expanding on a result of Borsuk.

Interpreting reflexive theories in finitely many axioms

V. Shavrukov (1997)

Fundamenta Mathematicae

Similarity:

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 1 (as well as 1 ) sentences π such that GB interprets ZF+π is Σ 3 0 -complete.

Cofinal Σ 1 1 and Π 1 1 subsets of ω ω

Gabriel Debs, Jean Saint Raymond (1999)

Fundamenta Mathematicae

Similarity:

We study properties of 1 1 and π 1 1 subsets of ω ω 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 " α ω ω , ω ω L ( α ) is bounded for ≤*".

On sums of two cubes: an Ω₊-estimate for the error term

M. Kühleitner, W. G. Nowak, J. Schoissengeier, T. D. Wooley (1998)

Acta Arithmetica

Similarity:

The arithmetic function r k ( n ) 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 r k ( n ) leads in a natural way to a certain error term P k ( t ) which is known to be O ( t 1 / 4 ) in mean-square. In this article it is proved that P ( t ) = Ω ( t 1 / 4 ( l o g l o g t ) 1 / 4 ) 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...

The minimum uniform compactification of a metric space

R. Grant Woods (1995)

Fundamenta Mathematicae

Similarity:

It is shown that associated with each metric space (X,d) there is a compactification u d X 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 u d X are presented, and a detailed study of the structure of u d X is undertaken. This culminates in a topological characterization of the outgrowth u d n n , where ( n , d ) is Euclidean n-space with its usual metric. ...

Difference functions of periodic measurable functions

Tamás Keleti (1998)

Fundamenta Mathematicae

Similarity:

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 Δ h f ( x ) = f ( x + h ) - f ( x ) 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, ( , G ) = H / : ( f G ) ( h H ) Δ h f G , 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 𝕋 = / that are invariant for changes on null-sets...

A functional S-dual in a strong shape category

Friedrich Bauer (1997)

Fundamenta Mathematicae

Similarity:

In the S-category P (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 D X , X = ( X , n ) P , turns out to be of the same weak homotopy type as an appropriately defined functional dual ( S 0 ) X ¯ (Corollary 4.9). Sometimes the functional object X Y ¯ is of the same weak homotopy type as the “real” function space X Y (§5).

Types on stable Banach spaces

José Iovino (1998)

Fundamenta Mathematicae

Similarity:

 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 X ^ is an ultrapower of X and B is a ball in X ^ , 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...

Countable partitions of the sets of points and lines

James Schmerl (1999)

Fundamenta Mathematicae

Similarity:

The following theorem is proved, answering a question raised by Davies in 1963. If L 0 L 1 L 2 . . . is a partition of the set of lines of n , then there is a partition n = S 0 S 1 S 2 . . . such that | S i | 2 whenever L i . There are generalizations to some other, higher-dimensional subspaces, improving recent results of Erdős, Jackson Mauldin.

The Arkhangel'skiĭ–Tall problem under Martin’s Axiom

Gary Gruenhage, Piotr Koszmider (1996)

Fundamenta Mathematicae

Similarity:

We show that MA σ - c e n t e r e d ( ω 1 ) implies that normal locally compact metacompact spaces are paracompact, and that MA( ω 1 ) 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.