共查询到20条相似文献,搜索用时 31 毫秒
1.
We study oscillation in the prefix-free complexity of initial segments of 1-random reals. For upward oscillations, we prove that ∑n∈ω2−g(n) diverges iff (∃∞n)K(X?n)>n+g(n) for every 1-random X∈ω2. For downward oscillations, we characterize the functions g such that (∃∞n)K(X?n)<n+g(n) for almost every X∈ω2. The proof of this result uses an improvement of Chaitin's counting theorem—we give a tight upper bound on the number of strings σ∈n2 such that K(σ)<n+K(n)−m.The work on upward oscillations has applications to the K-degrees. Write XK?Y to mean that K(X?n)?K(Y?n)+O(1). The induced structure is called the K-degrees. We prove that there are comparable () 1-random K-degrees. We also prove that every lower cone and some upper cones in the 1-random K-degrees have size continuum.Finally, we show that it is independent of ZFC, even assuming that the Continuum Hypothesis fails, whether all chains of 1-random K-degrees of size less than ℵ02 have a lower bound in the 1-random K-degrees. 相似文献
2.
M. M. Sheremeta 《Ukrainian Mathematical Journal》1996,48(1):130-139
We prove that if ω(t, x, K 2 (m) )?c(x)ω(t) for allxε[a, b] andx ε [0,b-a] wherec ∈L 1(a, b) and ω is a modulus of continuity, then λ n =O(n ?m-1/2ω(1/n)) and this estimate is unimprovable. 相似文献
3.
We show that for every Borel-measurable mapping Δ: [ω]ω → there exists A ∈ [ω]ω and there exists a continuous mapping Γ: [A]ω → [A]?ω with Γ(X) ? X such that for all X, Y ∈ [A]ω it follows that Δ(X) = Δ(Y) if Γ(X) = Γ(Y). In a sense, this is generalization of the Erdös-Rado canonization theorem 相似文献
4.
Yoav Benyamini 《Constructive Approximation》1985,1(1):217-229
The existence of best compact approximations for all bounded linear operators fromX intoC(K) is related to the behavior of asymptotic centers inX *. IfK is just one convergent sequence, the condition is that everyω *-convergent sequence inX * will have an asymptotic center. We first study this property, solving some open problems in the theory of asymptotic centers. IfK is more “complex,” the asymptotic centers should behave “continuously.” We use this observation to construct operators fromC[0,1] intoC(ω 2) and from ?1 intoL 1 without best compact approximation. We also construct spacesX 1,X 2, isomorphic to a Hilbert space, and operatorsT 1,∶X 1→C(ω 2),T 2∶?1→X 2 without best compact approximations. 相似文献
5.
《Topology and its Applications》1988,28(1):17-21
In [6], we defined an adequate index n(P) for 1-dimensional compact connected polyhedron P and we showed that Fd ω−1(t) ⩽ n(P) − 1 for any Whitney map ω for C(P) and any t ∈ [0, ω(P)]. In this paper, we show that the similar result is not always true if P is any n-dimensional compact connected polyhedron (n ⩾ 2). In fact, we show the following: Let P be any n-dimensional compact connected polyhedron (n ⩾ 2). Let m be any natural number such that m ⩾ 2. Then there exists a Whitney map ω for C(P) such that the m-sphere Sm is homotopically dominated by ω−1(t) for some t ∈ (0, ω(P)). In particular, Fd ω−1(t) ⩾ m. 相似文献
6.
Komjáth in 1984 proved that, for each sequence (An) of analytic subsets of a Polish space X, if lim supn∈HAn is uncountable for every H∈ω[N] then ?n∈GAn is uncountable for some G∈ω[N]. This fact, by our definition, means that the σ-ideal [X]?ω has property (LK). We prove that every σ-ideal generated by X/E has property (LK), for an equivalence relation E⊂X2 of type Fσ with uncountably many equivalence classes. We also show the parametric version of this result. Finally, the invariance of property (LK) with respect to various operations is studied. 相似文献
7.
Let K(2?) be the class of compact subsets of the Cantor space 2?, furnished with the Hausdorff metric. Let f ∈ C(2?). We study the map ω f : 2 ? → K(2?) defined as ω f (x) = ω(x, f), the ω-limit set of x under f. Unlike the case of n-dimensional manifolds, n ≥ 1, we show that ω f is continuous for the generic self-map f of the Cantor space, even though the set of functions for which ω f is everywhere discontinuous on a subsystem is dense in C(2?). The relationships between the continuity of ω f and some forms of chaos are investigated. 相似文献
8.
Doyel Barman 《Topology and its Applications》2012,159(3):806-813
We continue the study of Selectively Separable (SS) and, a game-theoretic strengthening, strategically selectively separable spaces (SS+) (see Barman, Dow (2011) [1]). The motivation for studying SS+ is that it is a property possessed by all separable subsets of Cp(X) for each σ-compact space X. We prove that the winning strategy for countable SS+ spaces can be chosen to be Markov. We introduce the notion of being compactlike for a collection of open sets in a topological space and with the help of this notion we prove that there are two countable SS+ spaces such that the union fails to be SS+, which contrasts the known result about SS spaces. We also prove that the product of two countable SS+ spaces is again countable SS+. One of the main results in this paper is that the proper forcing axiom, PFA, implies that the product of two countable Fréchet spaces is SS, a statement that was shown in Barman, Dow (2011) [1] to consistently fail. An auxiliary result is that it is consistent with the negation of CH that all separable Fréchet spaces have π-weight at most ω1. 相似文献
9.
A. A. Fora 《Periodica Mathematica Hungarica》1985,16(2):97-113
In this paper, we definen-segmentwise metric spaces and then we prove the following results:
- (i)|Let (X, d) be ann-segmentwise metric space. ThenX n has the fixed point property with respect to uniformly continuous bounded functions if and only if, for any continuous functionF: C *(X) → C*(X) and for anyn-tuple of distinct points x1, x2, ?, xn ∈X, there exists anh ∈C *(X) such that $$F(h)(x_1 ) = h(x_1 ),i = 1,2,...,n;$$ whereC *(X) has either the uniform topology or the subspace product (Tychonoff) topology \((C^ * (X) \subseteq X^X )\) .
- LetX i (i = 1, 2, ?) be countably compact Hausdorff spaces such thatX 1 × ? × Xn has the fixed point property for alln ∈N Then the product spaceX 1 × X2 × ? has the fixed point property. We shall also discuss several problems in the Fixed Point Theory and give examples if necessary. Among these examples, we have:
- There exists a connected metric spaceX which can be decomposed as a disjoint union of a closed setA and an open setB such thatA andB have the fixed point property andX does not have.
- There exists a locally compact metrizable spaceX which has the fixed point property but its one-point compactificationX + does not have the fixed point property.
10.
Jack T. Goodykoontz 《Topology and its Applications》1983,15(2):131-150
Let X be a metric continuum and 2x (C(X)) denote the hyperspace of closed subsets (subcontinua) of X. The concept of arc-smoothness, which is a special type of contractibility, is investigated in 2x and C(X). Results are obtained about hyperspaces of locally connected continua, about continua for which C(X) and the cone over X are homeomorphic, about Whitney levels in C(X), and about hyperspaces of hereditarily indecomposable continua. Some examples are given and several natural questions are raised. 相似文献
11.
Nicholas J. Kuhn 《Advances in Mathematics》2006,201(2):318-378
Let K(n) be the nth Morava K-theory at a prime p, and let T(n) be the telescope of a vn-self map of a finite complex of type n. In this paper we study the K(n)*-homology of Ω∞X, the 0th space of a spectrum X, and many related matters.We give a sampling of our results.Let PX be the free commutative S-algebra generated by X: it is weakly equivalent to the wedge of all the extended powers of X. We construct a natural map
sn(X):LT(n)P(X)→LT(n)Σ∞(Ω∞X)+ 相似文献
12.
《Journal of Complexity》1995,11(1):174-193
Let W ⊂ Rn be a semialgebraic set defined by a quantifier-free formula with k atomic polynomials of the kind f ∈ Z[X1, . . . , Xn] such that degX1, . . . , Xn(f) < d and the absolute values of coefficients of f are less than 2M for some positive integers d, M. An algorithm is proposed for producing the complexification, Zariski closure, and also for finding all irreducible components of W. The running time of the algorithm is bounded from above by MO(1)(kd)nO(1). The procedure is applied to computing a Whitney system for a semialgebraic set and the real radical of a polynomial ideal. 相似文献
13.
Sergio Macías 《Topology and its Applications》2007,154(1):39-53
Let X be a continuum. The n-fold hyperspace Cn(X), n<∞, is the space of all nonempty compact subsets of X with the Hausdorff metric. Four types of local connectivity at points of Cn(X) are investigated: connected im kleinen, locally connected, arcwise connected im kleinen and locally arcwise connected. Characterizations, as well as necessary or sufficient conditions, are obtained for Cn(X) to have one or another of the local connectivity properties at a given point. Several results involve the property of Kelley or C*-smoothness. Some new results are obtained for C(X), the space of subcontinua of X. A class of continua X is given for which Cn(X) is connected im kleinen only at subcontinua of X and for which any two such subcontinua must intersect. 相似文献
14.
Let k ? k′ be a field extension. We give relations between the kernels of higher derivations on k[X] and k′[X], where k[X]:= k[x 1,…, x n ] denotes the polynomial ring in n variables over the field k. More precisely, let D = {D n } n=0 ∞ a higher k-derivation on k[X] and D′ = {D′ n } n=0 ∞ a higher k′-derivation on k′[X] such that D′ m (x i ) = D m (x i ) for all m ? 0 and i = 1, 2,…, n. Then (1) k[X] D = k if and only if k′[X] D′ = k′; (2) k[X] D is a finitely generated k-algebra if and only if k′[X] D′ is a finitely generated k′-algebra. Furthermore, we also show that the kernel k[X] D of a higher derivation D of k[X] can be generated by a set of closed polynomials. 相似文献
15.
D. Barnes 《Journal of Pure and Applied Algebra》2009,213(5):846-856
If C is a stable model category with a monoidal product then the set of homotopy classes of self-maps of the unit forms a commutative ring, [S,S]C. An idempotent e of this ring will split the homotopy category: [X,Y]C≅e[X,Y]C⊕(1−e)[X,Y]C. We prove that provided the localised model structures exist, this splitting of the homotopy category comes from a splitting of the model category, that is, C is Quillen equivalent to LeSC×L(1−e)SC and [X,Y]LeSC≅e[X,Y]C. This Quillen equivalence is strong monoidal and is symmetric when the monoidal product of C is. 相似文献
16.
The aim of this paper is to prove that if a planar set A has a difference set Δ(A) satisfying Δ(A) ? ?+ + s for suitable s then A has at most 3 elements. This result is motivated by the conjecture that the disk has no more than 3 orthogonal exponentials. Further, we prove that if A is a set of exponentials mutually orthogonal with respect to any symmetric convex set K in the plane with a smooth boundary and everywhere non-vanishing curvature, then #(A ∩ [?q, q]2) ≦ C(K) q where C(K) is a constant depending only on K. This extends and clarifies in the plane the result of Iosevich and Rudnev. As a corollary, we obtain the result from [8] and [9] that if K is a centrally symmetric convex body with a smooth boundary and non-vanishing curvature, then L 2(K) does not possess an orthogonal basis of exponentials. 相似文献
17.
Let Kn denote the set of all n × n nonnegative matrices whose entries have sum n, and let ϕ be a real function on Kn defined by ϕ (X) = Πni=1Σnj=1xij + Πnj=1Σni=1xij − per X for X = [xij] ϵ Kn. A matrix A ϵ Kn is called a ϕ -maximizing matrix on Kn if ϕ (A) ⩾ ϕ (X) for all X ϵ Kn. It is conjectured that Jn = [1/n]n × n is the unique ϕ-maximizing matrix on Kn. In this note, the following are proved: (i) If A is a positive ϕ-maximizing matrix, then A = Jn. (ii) If A is a row stochastic ϕ-maximizing matrix, then A = Jn. (iii) Every row sum and every column sum of a ϕ-maximizing matrix lies between 1 − √2·n!/nn and 1 + (n − 1)√2·n!/nn. (iv) For any p.s.d. symmetric A ϵ Kn, ϕ (A) ⩽ 2 − n!/nn with equality iff A = Jn. (v) ϕ attains a strict local maximum on Kn at Jn. 相似文献
18.
In this article, we study the semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k(x) in the linear parabolic equation ut(x,t)=(k(x)uxx(x,t)), with Dirichlet boundary conditions u(0,t)=ψ0, u(1,t)=ψ1. Main goal of this study is to investigate the distinguishability of the input-output mappings Φ[⋅]:K→C1[0,T], Ψ[⋅]:K→C1[0,T] via semigroup theory. In this paper, we show that if the null space of the semigroup T(t) consists of only zero function, then the input-output mappings Φ[⋅] and Ψ[⋅] have the distinguishability property. Moreover, the values k(0) and k(1) of the unknown diffusion coefficient k(x) at x=0 and x=1, respectively, can be determined explicitly by making use of measured output data (boundary observations) f(t):=k(0)ux(0,t) or/and h(t):=k(1)ux(1,t). In addition to these, the values k′(0) and k′(1) of the unknown coefficient k(x) at x=0 and x=1, respectively, are also determined via the input data. Furthermore, it is shown that measured output dataf(t) and h(t) can be determined analytically, by an integral representation. Hence the input-output mappings Φ[⋅]:K→C1[0,T], Ψ[⋅]:K→C1[0,T] are given explicitly in terms of the semigroup. Finally by using all these results, we construct the local representations of the unknown coefficient k(x) at the end points x=0 and x=1. 相似文献
19.
Risong Li 《Communications in Nonlinear Science & Numerical Simulation》2012,17(7):2815-2823
Let f : X → X be a continuous map of a compact metric space X. The map f induces in a natural way a map fM on the space M(X) of probability measures on X, and a transformation fK on the space K(X) of closed subsets of X. In this paper, we show that if (X, f) is a chain transitive system with shadowing property, then exactly one of the following two statements holds:
- (a)
- fn and (fK)n are syndetically sensitive for all n ? 1.
- (b)
- fn and (fK)n are equicontinuous for all n ? 1.
20.
Mar Jiménez-Sevilla 《Journal of Mathematical Analysis and Applications》2011,378(1):173-183
Let us consider a Banach space X with the property that every real-valued Lipschitz function f can be uniformly approximated by a Lipschitz, C1-smooth function g with Lip(g)?CLip(f) (with C depending only on the space X). This is the case for a Banach space X bi-Lipschitz homeomorphic to a subset of c0(Γ), for some set Γ, such that the coordinate functions of the homeomorphism are C1-smooth (Hájek and Johanis, 2010 [10]). Then, we prove that for every closed subspace Y⊂X and every C1-smooth (Lipschitz) function f:Y→R, there is a C1-smooth (Lipschitz, respectively) extension of f to X. We also study C1-smooth extensions of real-valued functions defined on closed subsets of X. These results extend those given in Azagra et al. (2010) [4] to the class of non-separable Banach spaces satisfying the above property. 相似文献