共查询到20条相似文献,搜索用时 10 毫秒
1.
With the use of directed graphs, we study topologies on finite sets. On this basis, we propose a new classification of these
topologies. Some properties of T
0-topologies on finite sets are proved. In particular, we prove the existence, in T
0-topologies, of open sets containing any number of elements that does not exceed the cardinality of the set itself.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 7, pp. 992–996, July, 2008. 相似文献
2.
&#;kos Cs&#;sz&#;r 《Acta Mathematica Hungarica》2005,106(1-2):53-66
Summary We study the even power means of a sum analogous to Dedekind sums, and give a sharp asymptotic formula. 相似文献
3.
Olga Polverino 《Discrete Mathematics》2010,310(22):3096-3107
In this paper linear sets of finite projective spaces are studied and the “dual” of a linear set is introduced. Also, some applications of the theory of linear sets are investigated: blocking sets in Desarguesian planes, maximum scattered linear sets, translation ovoids of the Cayley Hexagon, translation ovoids of orthogonal polar spaces and finite semifields. Besides “old” results, new ones are proven and some open questions are discussed. 相似文献
4.
Laurence Kirby 《Archive for Mathematical Logic》2008,47(2):143-157
This article defines a hierarchy on the hereditarily finite sets which reflects the way sets are built up from the empty set
by repeated adjunction, the addition to an already existing set of a single new element drawn from the already existing sets.
The structure of the lowest levels of this hierarchy is examined, and some results are obtained about the cardinalities of
levels of the hierarchy.
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5.
In this paper, we study the relations of the sizes of various sections of finite linear groups and the largest orbit size of the linear group actions. We also study various applications of those orbit theorems. 相似文献
6.
Antonio Maschietti 《Journal of Combinatorial Theory, Series A》2011,118(1):228-230
We construct Kakeya sets in AG(n,q), where q is even and n?2, whose points are zeros of a polynomial of degree q. 相似文献
7.
Assaf Rinot 《Archive for Mathematical Logic》2007,46(5-6):457-464
In their paper from 1981, Milner and Sauer conjectured that for any poset , if , then P must contain an antichain of size κ. We prove that for λ > cf(λ) = κ, if there exists a cardinal μ < λ such that cov(λ, μ, κ, 2) = λ, then any poset of cofinality λ contains λ
κ
antichains of size κ. The hypothesis of our theorem is very weak and is a consequence of many well-known axioms such as GCH, SSH and PFA. The
consistency of the negation of this hypothesis is unknown.
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8.
9.
本文将给出偏序集零调与可缩的几个充分条件,它们包含和深化了文[1]和[2]中的一些结果,把[2]中的一些结果推广到无限偏序集的情形. 相似文献
10.
Dikran Dikranjan Anna Giordano Bruno 《Topology and its Applications》2011,158(17):2391-2407
In the general context of functorial topologies, we prove that in the lattice of all group topologies on an abelian group, the infimum between the Bohr topology and the natural topology is the profinite topology. The profinite topology and its connection to other functorial topologies is the main objective of the paper. We are particularly interested in the poset C(G) of all finite-index subgroups of an abelian group G, since it is a local base for the profinite topology of G. We describe various features of the poset C(G) (its cardinality, its cofinality, etc.) and we characterize the abelian groups G for which C(G)?{G} is cofinal in the poset of all subgroups of G ordered by inclusion. Finally, for pairs of functorial topologies T, S we define the equalizer E(T,S), which permits to describe relevant classes of abelian groups in terms of functorial topologies. 相似文献
11.
Francis Jordan 《Topology and its Applications》2010,157(15):2392-1968
Let C(X,Y) be the set of all continuous functions from a topological space X into a topological space Y. We find conditions on X that make the Isbell and fine Isbell topologies on C(X,Y) equal for all Y. For zero-dimensional spaces X, we show there is a space Z such that the coincidence of the Isbell and fine Isbell topologies on C(X,Z) implies the coincidence on C(X,Y) for all Y. We then consider the question of when the Isbell and fine Isbell topologies coincide on the set of continuous real-valued functions. Our results are similar to results established for consonant spaces. 相似文献
12.
13.
This is a survey of known results and still open problems on antipodal properties of finite sets in Euclidean space. The exposition follows historical lines and takes into consideration both metric and affine aspects. 相似文献
14.
We prove that a relation over is recursively enumerable if and only if it is Diophantine over . We do this by first constructing a model of in , where n is represented by Zn. In a second step, we show that it suffices to eliminate a bounded universal quantifier. Then finally, the hardest part of the proof is to show that we can eliminate this quantifier. 相似文献
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17.
Let R be a finite principal ideal ring and positive integers. In this paper, we study the matrix graph over R which is the graph whose vertices are matrices over R and two matrices A and B are adjacent if and only if . We show that this graph is a connected vertex transitive graph. The distance, diameter, independence number, clique number and chromatic number of this graph are also determined. This graph can be applied to study MRD codes over R. We obtain that a maximal independent set of the matrix graph is a maximum rank distance (MRD) code and vice versa. Moreover, we show the existence of linear MRD codes over R. 相似文献
18.
Abstract Eisenbud et al. proved a number of results regarding Gröbner bases and initial ideals of those ideals J in the free associative algebra K ?X 1,…, X n ? which contain the commutator ideal. We prove similar results for ideals which contains the anti-commutator ideal (the defining ideal of the exterior algebra). We define one weak notion of generic initial ideals in K ?X 1,…, X n ?, and show that generic initial ideals of ideals containing the anti-commutator ideal, or the commutator ideal, are finitely generated. 相似文献
19.
In this paper, the homogeneous weights of matrix product codes over finite principal ideal rings are studied and a lower bound for the minimum homogeneous weights of such matrix product codes is obtained. 相似文献
20.
Computability of measurable sets via effective topologies 总被引:1,自引:0,他引:1
We investigate in the frame of TTE the computability of functions of the measurable sets from an infinite computable measure
space such as the measure and the four kinds of set operations. We first present a series of undecidability and incomputability
results about measurable sets. Then we construct several examples of computable topological spaces from the abstract infinite
computable measure space, and analyze the computability of the considered functions via respectively each of the standard
representations of the computable topological spaces constructed.
The authors are supported by grants of NSFC and DFG. 相似文献