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1.
We consider the stable homotopy category S of polyhedra (finite cell complexes). We say that two polyhedra X,Y are in the same genus and write XY if X p Y p for all prime p, where X p denotes the image of Xin the localized category S p . We prove that it is equivalent to the stable isomorphism XB 0YB 0, where B 0 is the wedge of all spheres S n such that π n S (X) is infinite. We also prove that a stable isomorphism XXYX implies a stable isomorphism XY.  相似文献   

2.
LetA andB be two reduced commutative rings with finitely many minimal prime ideals. If the polynomial algebrasA[X 1 …X n ]=B[Y 1 …Y n ] whereX i ,Y iF are variables overA andB respectively, then there exists an injective ring homomorphism ϕ:AB such thatB is finitely generated over ϕ(A).  相似文献   

3.
Ergodic homeomorphisms T and S of Polish probability spaces X and Y are evenly Kakutani equivalent if there is an orbit equivalence ϕ: X 0Y 0 between full measure subsets of X and Y such that, for some AX 0 of positive measure, ϕ restricts to a measurable isomorphism of the induced systems T A and S ϕ(A). The study of even Kakutani equivalence dates back to the seventies, and it is well known that any two irrational rotations of the circle are evenly Kakutani equivalent. But even Kakutani equivalence is a purely measurable relation, while systems such as irrational rotations are both measurable and topological.  相似文献   

4.
Whenϕ is an analytic map of the unit diskU into itself, andX is a Banach space of analytic functions onU, define the composition operatorC ϕ byC ϕ (f)=f o ϕ, forfX. In this paper we show how to use the Calderón theory of complex interpolation to obtain information on the spectrum ofC ϕ (under suitable hypotheses onϕ) acting on the Bloch spaceB and BMOA, the space of analytic functions in BMO. To do this we first obtain some results on the essential spectral radius and spectrum ofC ϕ on the Bergman spacesA pand Hardy spacesH p,spaces which are connected toB and BMOA by the interpolation relationships [A 1,B] t =A pand [H 1,BMOA] t =H pfor 1=p(1−t).  相似文献   

5.
6.
For a fibre preserving map ϕ: EE on a fibration (E, π, B), we construct a grading preserving map T(ϕ, π) between H*(E) and H*(B) that generalizes the Lefschetz number. If T(ϕ, π) is an isomorphism between H 0(E) and H 0(B), then π restricts to a surjective local diffeomorphism on each connected component of the fixed point set of ϕ under a transversality condition. This yields a characterization for the bundle HGG/H to be trivial when π 1 (G/H) = 0.  相似文献   

7.
The set of difunctional binary relations DX plays a special role in representing inverse semigroups by binary relations. However, DX is not an inverse semigroup either with the standard operation ∘, or with an alternative operation introduced in [6]. We introduce a new binary operation ⋄ on the set BX of binary relations. We demonstrate that (DX, ⋄) is an inverse semigroup, and the symmetric inverse semigroup (IX, ∘) is a subsemigroup of (DX,⋄).  相似文献   

8.
Let X be a metrizable space and let φ:R× X → X be a continuous flow on X. For any given {φt}-invariant Borel probability measure, this paper presents a {φt}-invariant Borel subset of X satisfying the requirements of the classical ergodic theorem for the contiImous flow (X, {φt}). The set is more restrictive than the ones in the literature, but it might be more useful and convenient, particularly for non-uniformly hyperbolic systems and skew-product flows.  相似文献   

9.
Let A and B be standard operator algebras on Banach spaces X and Y, respectively. The peripheral spectrum σπ (T) of T is defined by σπ (T) = z ∈ σ(T): |z| = maxw∈σ(T) |w|. If surjective (not necessarily linear nor continuous) maps φ, ϕ: AB satisfy σπ (φ(S)ϕ(T)) = σπ (ST) for all S; TA, then φ and ϕ are either of the form φ(T) = A 1 TA 2 −1 and ϕ(T) = A 2 TA 1 −1 for some bijective bounded linear operators A 1; A 2 of X onto Y, or of the form φ(T) = B 1 T*B 2 −1 and ϕ(T) = B 2 T*B −1 for some bijective bounded linear operators B 1;B 2 of X* onto Y.   相似文献   

10.
Let C be an Abelian group. An Abelian group A from a class X of Abelian groups is said to be C H-definable in X if, for any group BX, the isomorphism Hom(C,A) ≅ Hom(C,B) implies that AB. If every group from X is C H-definable in X, then X is called an C H-class. In this paper, we study conditions under which a class of completely decomposable torsion-free Abelian groups is an C H-class, where C is a vector group.  相似文献   

11.
Even Set Systems     
In phylogenetic combinatorics, the analysis of split systems is a fundamental issue. Here, we observe that there is a canonical one-to-one correspondence between split systems on the one, and “even” set systems on the other hand, i.e., given any finite set X, we show that there is a canonical one-to-one correspondence between the set P (S (X ) ){\mathcal P (\mathcal S (X ) )} consisting of all subsets S{\mathcal S} of the set S (X){\mathcal S (X)} of all splits of the set X (that is, all 2-subsets {A, B}{\{A, B\}} of the power set P (X){\mathcal P (X)} of X for which AB = X and AB = 0̸ hold) and the set P even (P (X)){\mathcal P ^{even} (\mathcal P (X))} consisting of all subsets E of the power set P (X){\mathcal P (X)} of X for which, for each subset Y of X, the number of proper subsets of Y contained in E is even.  相似文献   

12.
Let φ be a Hausdorff measure function and A be an infinite increasing sequence of positive integers. The Hausdorff-type measure φ - mA associated to φ and A is studied. Let X(t)(t ∈ R^N) be certain Gaussian random fields in R^d. We give the exact Hausdorff measure of the graph set GrX([0, 1]N), and evaluate the exact φ - mA measure of the image and graph set of X(t). A necessary and sufficient condition on the sequence A is given so that the usual Hausdorff measure function for X([0, 1] ^N) and GrX([0, 1]^N) are still the correct measure functions. If the sequence A increases faster, then some smaller measure functions will give positive and finite ( φ A)-Hausdorff measure for X([0, 1]^N) and GrX([0, 1]N).  相似文献   

13.
We investigate the adjoints of linear fractional composition operators Cφ acting on classical Dirichlet space D(BN ) in the unit ball BN of CN , and characterize the normality and essential normality of Cφ on D(BN ) and the Dirichlet space modulo constant function D0(BN ), where φ is a linear fractional map of BN . In addition, we also show that for any non-elliptic linear fractional map φ of BN , the composition maps σ ο φ and φ ο σ are elliptic or parabolic linear fractional maps of BN .  相似文献   

14.
We force 2 λ to be large, and for many pairs in the interval (λ, 2 λ ) a strong version of the polarized partition relations holds. We apply this to problems in general topology. For example, consistently, every 2 λ is the successor of a singular and for every Hausdorff regular space X, hd(X) ≤ s(X)+3, hL(X) ≤ s(X)+3 and better when s(X) is regular, via a halfgraph partition relations. For the case s(X) = 0 we get hd(X), hL(X) ≤ N 2.  相似文献   

15.
We investigate the semigroups of full and partial transformations of a set X which preserve a binary relation σ defined on X. We consider in detail the case where σ is an order or a quasi-order relation. There are conditions of regularity of such semigroups. We introduce two definitions of preservation of σ for the semigroup of binary relations. It is proved that subsets of B(X) preserving σ are semigroups in each case. We give the condition of regularity of B σ (X) in the case where σ(X) is a quasi-order.  相似文献   

16.
Under the appropriate definition of sampling density Dϕ, a function f that belongs to a shift invariant space can be reconstructed in a stable way from its non-uniform samples only if Dϕ≥1. This result is similar to Landau's result for the Paley-Wiener space B 1/2 . If the shift invariant space consists of polynomial splines, then we show that Dϕ<1 is sufficient for the stable reconstruction of a function f from its samples, a result similar to Beurling's special case B 1/2 .  相似文献   

17.
A directed triple system of order v with index λ, briefly by DTS(v,λ), is a pair (X, B) where X is a v-set and B is a collection of transitive triples (blocks) on X such that every ordered pair of X belongs to λ blocks of B. A simple DTS(v, λ) is a DTS(v, λ) without repeated blocks. A simple DTS(v, ),) is called pure and denoted by PDTS(v, λ) if (x, y, z) ∈ B implies (z, y, x), (z, x, y), (y, x, z), (y, z, x), (x, z, y) B. A large set of disjoint PDTS(v, λ), denoted by LPDTS(v, λ), is a collection of 3(v - 2)/λ disjoint pure directed triple systems on X. In this paper, some results about the existence for LPDTS(v, λ) are presented. Especially, we determine the spectrum of LPDTS(v, 2).  相似文献   

18.
Let B be a Blaschke product with simple zeros in the unit disk, let Λ be the set of its zeros, and let ϕ∈H. It is known that ϕ+BH is a weak* generator of the algebra H/BH if (for B that satisfy the Carleson condition (C)) and only if the sequence ϕ(Λ) is a weak* generator of the algebra l. In this paper, we show that for any Blaschke product B with simple zeros that does not satisfy condition (C), there exists B=B1·…·BN, where N ∈ℕ, and B1, …, BN are Blaschke products satisfying condition (C), there exists a function ϕ∈H such that ϕ(Λ) is a weak* generator of the algebra l, and ϕ+BH is not a weak* generator of the algebra H/BH. Bibliography: 12 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 232, 1996, pp. 73–85. Translated by M. F. Gamal'.  相似文献   

19.
20.
A covering p from a Cayley graph Cay(G, X) onto another Cay(H, Y) is called typical Frobenius if G is a Frobenius group with H as a Frobenius complement and the map p : G →H is a group epimorphism. In this paper, we emphasize on the typical Frobenius coverings of Cay(H, Y). We show that any typical Frobenius covering Cay(G, X) of Cay(H, Y) can be derived from an epimorphism /from G to H which is determined by an automorphism f of H. If Cay(G, X1) and Cay(G, X2) are two isomorphic typical Frobenius coverings under a graph isomorphism Ф, some properties satisfied by Фare given.  相似文献   

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