共查询到20条相似文献,搜索用时 15 毫秒
1.
We give a wedge removability theorem for metrically thin sets of two codimensional Hausdorff null measure. Following [22],
this removability theorem combined with the wedge removability theorem of [21] for closed subsets of two codimensional manifolds,
gives a CR-meromorphic extension theorem in the greater codimensional case.
Received: 28 August 1999; in final form: 10 April 2000 / Published online: 17 May 2001 相似文献
2.
Jörg Winkelmann 《Mathematische Zeitschrift》2001,236(4):883-901
We construct infinite discrete subsets of Stein manifolds with remarkable properties. These generalize results of Rosay and
Rudin on discrete subsets of .
Received August 21, 1998; in final form October 11, 1999 / Accepted Published online February 5, 2001 相似文献
3.
Lszl Liptk 《Discrete Mathematics》1997,170(1-3):203-209
We prove using a direct construction that one can choose n − 2 subsets of an n-element set with different cardinality such that none of them contains any other. As a generalization, we prove that if for any j we can have at most k subsets containing exactly j elements (k> 1), then for n 5 we can choose at most k(n − 3) subsets from an n-element set such that they form a Sperner system. Moreover, we prove that this can be achieved if n is large enough, and give a construction for n 8k − 4. 相似文献
4.
As modular and distributive ordered sets generalize modular and distributive lattices, it is a natural question to ask whether there exist some forbidden configurations for those ordered sets. We present such configurations in the form of strong subsets and LU subsets. 相似文献
5.
We present a form of the Mean Value Theorem (MVT) for a continuous function f between metric spaces, connecting it with the possibility to choose the relation of f in a homeomorphic way. We also compare our formulation of the MVT with the classic one when the metric spaces are open subsets of Banach spaces. As a consequence, we derive a version of the Mean Value Propriety for measure spaces that also possesses a compatible metric structure. 相似文献
6.
Kyriakos Keremedis Eleftherios Tachtsis 《Proceedings of the American Mathematical Society》2005,133(12):3691-3701
In the framework of ZF, i.e., Zermelo-Fraenkel set theory without the axiom of choice AC, we show that if the family of all non-empty, closed subsets of a metric space has a choice function, then so does the family of all non-empty, open subsets of . In addition, we establish that the converse is not provable in ZF.
We also show that the statement ``every subspace of the real line with the standard topology has a choice function for its family of all closed, non-empty subsets" is equivalent to the weak choice form ``every continuum sized family of non-empty subsets of reals has a choice function".
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8.
Victor D. Didenko 《Complex Analysis and Operator Theory》2008,2(2):345-359
Two types of estimate for the spectral radius of the multivariate refinement operator with power diagonal dilations are presented.
One type contains multiplicator norm of number matrices generated by the symbol of the corresponding operator and by specific
subsets of repeating fractions. These subsets are used together with the little Fermat theorem to establish estimates that
comprise integrals over tori of various dimensions. Moreover, we note certain classes of symbols when the exact value of the
spectral radius of refinement operator can be found. For the spectral radius of subdivision operators point value estimates
are established.
Submitted: April 25, 2007. Accepted: November 5, 2007. 相似文献
9.
Andreas Gastel 《Mathematische Zeitschrift》2002,242(1):47-62
By constructing examples which are explicit up to solving an ODE, we prove that singularities of first kind exist for the
harmonic map and Yang-Mills heat flows. As a by-product, we also get a simplified proof of Ratto's/Ding's theorem about the
existence of harmonic Hopf constructions.
Received: 25 May 2000; in final form: 17 November 2000 / Published online: 25 June 2001 相似文献
10.
This work concerns constructive aspects of measure theory. By considering metric completions of Boolean algebras – an approach
first suggested by Kolmogorov – one can give a very simple construction of e.g. the Lebesgue measure on the unit interval.
The integration spaces of Bishop and Cheng turn out to give examples of such Boolean algebras. We analyse next the notion
of Borel subsets. We show that the algebra of such subsets can be characterised in a pointfree and constructive way by an
initiality condition. We then use our work to define in a purely inductive way the measure of Borel subsets.
Received: 9 November 2000 / Revised version: 23 March 2001 / Published online: 12 July 2002 相似文献
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12.
A. I. Stukachyov 《Algebra and Logic》2002,41(2):127-139
13.
Summary. We consider random walks with a bias toward the root on the family tree T of a supercritical Galton–Watson branching process and show that the speed is positive whenever the walk is transient. The
corresponding harmonic measures are carried by subsets of the boundary of dimension smaller than that of the whole boundary.
When the bias is directed away from the root and the extinction probability is positive, the speed may be zero even though
the walk is transient; the critical bias for positive speed is determined.
Received: 7 July 1995 / In revised form: 9 January 1996 相似文献
14.
We investigate what can be when A is torsion-free and . We thereby give an answer to a question of Golasiński and Gon?alves which asks for the divisible Abelian groups which can
be the type of a co-Moore space.
Received: 25 January 2000; in final form: 20 June 2000 / Published online: 25 June 2001 相似文献
15.
Marilyn Breen 《Monatshefte für Mathematik》2003,139(2):105-109
Let S be a nonempty closed, simply connected set in the plane. For α > 0, let ℳ denote the family of all maximal subsets of S which are starshaped via paths of length at most α. Then ⋂{M : M in ℳ} is either starshaped via α-paths or empty. The result fails without the simple connectedness condition. However, even
with a simple connectedness requirement, there is no Helly theorem for intersections of sets which are starshaped via α-paths.
Received November 19, 2001; in revised form April 25, 2002
Published online November 18, 2002 相似文献
16.
In this paper we give first a new combinatorial interpretation of the coefficients of chromatic polynomials of graphs in terms of subsets of permutations. Motivated by this new interpretation, we introduce next a combinatorially defined polynomial associated to a directed graph, and prove that it is related to chromatic polynomials. These polynomials are a specialization of cover polynomials of digraphs.I am grateful to the Swiss National Science Foundation for its partial financial supportFinal version received: June 25, 2003 相似文献
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18.
Zbigniew Jelonek 《Mathematische Zeitschrift》2002,239(2):321-333
In this paper we study the set of points at which a real polynomial mapping is not proper.
Received: 7 May 1999; in final form: 18 September 2000 / Published online: 25 June 2001 相似文献
19.
The Riesz–Sobolev inequality provides a sharp upper bound for a trilinear expression involving convolution of indicator functions of sets. Equality is known to hold only for indicator functions of appropriately situated intervals. We characterize ordered triples of subsets of R~1 that nearly realize equality, with quantitative bounds of power law form with the optimal exponent. 相似文献
20.
Mark Pankov 《Results in Mathematics》2005,48(1-2):124-130
Let V and V′ be n-dimensional vector spaces. Let also Ω and Ω′ be non-degenerate symplectic forms defined on V and V′, respectively. Denote by Π and Π′ the projective spaces associated with V and V′. We put for the sets of k-dimensional totally isotropic subspaces of Π and Π′. We study mappings of BF03322901 which transfer base subsets to base subsets and show that such mappings are induced by strong embeddings of Π to Π′ if 3k + 3 ≤ n. 相似文献