共查询到20条相似文献,搜索用时 31 毫秒
1.
A space X is said to satisfy condition (C) if for every Y?X with |Y|=ω1, any family of open subsets of Y with ||=ω1 has a countable network. It is easy to see that if X satisfies condition (C), then its Pixley-Roy hyperspace [X] is CCC. We show that under MAω1 condition (C) is also necessary for [X] to be CCC, but under CH it is not. 相似文献
2.
R.Grant Woods 《Topology and its Applications》1985,21(3):287-295
Let be a closed-hereditary topological property preserved by products. Call a space -regular if it is homeomorphic to a subspace of a product of spaces with . Suppose that each -regular space possesses a -regular compactification. It is well-known that each -regular space X is densely embedded in a unique space γscPX with such that if f: X → Y is continuous and Y has , then f extends continuously to γscPX. Call -pseudocompact if γscPX is compact.Associated with is another topological property #, possessing all the properties hypothesized for above, defined as follows: a -regular space X has # if each -pseudocompact closed subspace of X is compact. It is known that the -pseudocompact spaces coincide with the #-pseudocompact spaces, and that # is the largest closed-hereditary, productive property for which this is the case. In this paper we prove that if is not the property of being compact and -regular, then # is not simply generated; in other words, there does not exist a space E such that the spaces with # are precisely those spaces homeomorphic to closed subspaces of powers of E. 相似文献
3.
C.D Godsil 《Journal of Combinatorial Theory, Series B》1980,29(1):116-140
Let X be a vertex-transitive graph with complement . We show that if both N, the neighbourhood of a vertex in X, and , the neighbourhood of a vertex in , are disconnected, then either X is isomorphic to K3 × K3 or both N and contain isolated vertices. We characterize the graphs which satisfy this last condition and show in consequence that they admit automorphisms of the form (12)(34). It follows that if X is a GRR for some graph G then at least one of N and is connected. (X is said to be a graphical regular representation, or GRR, for G if its automorphism group is isomorphic to G and acts regularly on its vertices.) Using this result we determine those groups generated by their involutions which do not have a GRR. The largest such group has order 18. As a corollary we conclude that all non-abelian simple groups have GRR's. 相似文献
4.
Laurence Boxer 《Topology and its Applications》1980,11(1):17-29
Let X be a finite-dimensional compactum. Let (X) and (X) be the spaces of retractions and non-deformation retractions of X, respectively, with the compact-open (=sup-metric) topology. Let 2Xh be the space of non-empty compact ANR subsets of X with topology induced by the homotopy metric. Let RXh be the subspace of 2Xh consisting of the ANR's in X that are retracts of X.We show that (Sm) is simply-connected for m > 1. We show that if X is an ANR and A0?RXh, then limi→∞Ai=A0 in 2Xh if and only if for every retraction r0 of X onto A0 there are, for almost all i, retractions ri of X onto Ai such that limi→∞ri=ro in (X). We show that if X is an ANR, then the local connectedness of (X) implies that of RXh. We prove that (M) is locally connected if M is a closed surface. We give examples to show how some of our results weaken when X is not assumed to be an ANR. 相似文献
5.
J.R. Tort 《Discrete Mathematics》1983,44(2):181-185
Let X be a set of n elements. Let 3(X) be the set of all triples of X. We define a clique as a set of triples which intersect pairwise in two elements. In this paper we prove that if n?6, the minimum cardinality of a partition of 3(X) into cliques is . 相似文献
6.
Let X(ω) be a random element taking values in a linear space endowed with the partial order ≤; let 0 be the class of nonnegative order-preserving functions on such that, for each g∈0, E[g(X)] is defined; and let 1?0 be the subclass of concave functions. A version of Markov's inequality for such spaces in P(X ≥ x) ≤ inf0E[g(X)]/g(x). Moreover, if E(X) = ξ is defined and if Jensen's inequality applies, we have a further inequality P(X≥x) ≤ inf1E[g(X)]/g(x) ≤ inf1g(ξ)/g(x). Applications are given using a variety or orderings of interest in statistics and applied probability. 相似文献
7.
R.A. Maller 《Stochastic Processes and their Applications》1980,10(1):65-73
We show that if Xi is a stationary sequence for which converges to a finite non zero random variable of constant sign, where Sn=X1+X2+?+Xn and Bn is a sequence of constants, then Bn is regularly varying with index 1. If in addition is finite, then is finite, and if in addition to this Xi satisfies an asymptotic independence condition, . 相似文献
8.
Jun Terasawa 《Topology and its Applications》1980,11(1):93-102
About spaces N∪ (see [2, Exercise 5I]), the following are proved: (1) dim , then no real-valued continuous fu ction on N∪ is onto (and hence, dim ), (3) any compact metric space without isolated points is homeomorphic to some and (4)there are spaces X,X1 and X2 of the form N∪ such that X=X1∪X2,X2andX2 are zero sets of X, and dim X=n, dimX1=dimX2=0, where n=1,2,… or ∞. 相似文献
9.
10.
Takemi Mizokami 《Topology and its Applications》1980,11(2):211-221
Let (A) be the characterization of dimension as follows: Ind X?n if and only if X has a σ-closure-preserving base such that Ind B(W)?n?1 for every W?. The validity of (A) is proved for spaces X such that(i) X is a paracompact σ-metric space with a scale {Xi} such that each Xi has a uniformly approaching anti-cover, or(ii) X is a subspace of the product ΠXi of countably many L-spaces Xi, the notion of which is due to K. Nagami.(i) and (ii) are the partial answers to Nagata's problem wheter (A) holds or not for every M1-space X. 相似文献
11.
Let X be a set. A collection of subsets of X has subinfinite rank if whenever ? , ∩≠ø, and is infinite, then there are two distinct elements of , one of which is a subset of the other. Theorem. AT1space with a base of subinfinite rank is hereditarily metacompact. 相似文献
12.
A completely regular space X is called nearly pseudocompact if υX?X is dense in βX?X, where βX is the Stone-?ech compactification of X and υX is its Hewitt realcompactification. After characterizing nearly pseudocompact spaces in a variety of ways, we show that X is nearly pseudocompact if it has a dense locally compact pseudocompact subspace, or if no point of X has a closed realcompact neighborhood. Moreover, every nearly pseudocompact space X is the union of two regular closed subsets X1, X2 such that Int X1 is locally compact, no points of X2 has a closed realcompact neighborhood, and . It follows that a product of two nearly pseudocompact spaces, one of which is locally compact, is also nearly pseudocompact. 相似文献
13.
Harald Brandenburg 《Topology and its Applications》1985,20(1):17-27
Following Pareek a topological space X is called D-paracompact if for every open cover of X there exists a continuous mapping f from X onto a developable T1-space Y and an open cover of Y such that { f-1[B]|B ∈ } refines . It is shown that a space is D-paracompact if and only if it is subparacompact and D-expandable. Moreover, it is proved that D-paracompactness coincides with a covering property, called dissectability, which was introduced by the author in order to obtain a base characterization of developable spaces. 相似文献
14.
Richard L. Tweedie 《Stochastic Processes and their Applications》1975,3(4):385-403
Let {Xn} be a ?-irreducible Markov chain on an arbitrary space. Sufficient conditions are given under which the chain is ergodic or recurrent. These extend known results for chains on a countable state space. In particular, it is shown that if the space is a normed topological space, then under some continuity conditions on the transition probabilities of {Xn} the conditions for ergodicity will be met if there is a compact set K and an ? > 0 such that whenever x lies outside K and is bounded, x ∈ K; whilst the conditions for recurrence will be met if there exists a compact K with for all x outside K. An application to queueing theory is given. 相似文献
15.
We show that CH implies that , when equipped with the Vietoris topology, has a subspace which is an L-space and a subspace which is an S-space. This is an immediate consequence of the following purely combinatorial result: CH implies the existence of an ω1-sequence 〈xα: α < ω1〉 in such that (1) if α<β<ω1, then ; (2) if I ?ω1 is unaccountable, then there are distinct α, β ∈ I with Xβ ?Xα. 相似文献
16.
H.H. Hung 《Topology and its Applications》1982,14(2):163-165
We propose a generalization of Heath's theorem that semi-metric spaces with point-countable bases are developable: A semi-metrizable space X is developabale if (and only if) there is on it a σ-discrete family of closed sets, interior-preserving over each member C of which is a countable family {n(C): n ∈ N} of collections of open sets such that if U is a neighbourhood of ξ∈X, then there are such a Γ∈ and such a v∈ N that ξ ? Γ and ξ∈ int ∩ (D: ξ: D∈v(Γ))?U. 相似文献
17.
Wolfgang Lusky 《Journal of Functional Analysis》1985,62(1):1-7
It is shown that every separable Banach space X containing a subspace isomorphic to c0 has a subspace Y with basis such that and the latter space has a shrinking basis and an unconditional FDD. Moreover, it is shown that X ⊕ C∞ has a basis if X has the bounded approximation property. 相似文献
18.
An essentially binormal operator on Hilbert space is an operator which is unitarily equivalent to a 2 × 2 matrix of essentially commuting, essentially normal operators. A natural invariant of essentially binormal operators up to unitary equivalence in the Calkin Algebra is the reducing essential 2 × 2 matricial spectrum. A nonempty compact subset X of the set of 2 × 2 matrices is called hypoconvex, if it is the reducing essential 2 × 2 matricial spectrum of an operator on Hilbert space. The set EN2(X) is then defined to be the set of all equivalence classes (up to unitary equivalence in the Calkin algebra) of essentially binormal operators whose reducing essential 2 × 2 matricial spectrum coincides with X. The aim of this paper is to prove a result that enables one to compute EN2(X) in terms of the topological structure of the space of unitary orbits of X. Indeed, it is shown that for every hypoconvex subset X of the set of 2 × 2 matrices, there exists a natural homomorphism from onto EN2(X). Also, a six term cyclic exact sequence is obtained, which produces a characterization of the kernel of the above-mentioned homomorphism. 相似文献
19.
Malcolm R. Adams 《Journal of Functional Analysis》1983,52(3):420-441
Let Q be a self-adjoint, classical, zeroth order pseudodifferential operator on a compact manifold X with a fixed smooth measure dx. We use microlocal techniques to study the spectrum and spectral family, {ES}S∈ as a bounded operator on L2(X, dx).Using theorems of Weyl (Rend. Circ. Mat. Palermo, 27 (1909), 373–392) and Kato (“Perturbation Theory for Linear Operators,” Springer-Verlag, 1976) on spectra of perturbed operators we observe that the essential spectrum and the absolutely continuous spectrum of Q are determined by a finite number of terms in the symbol expansion. In particular SpecESSQ = range(q(x, ξ)) where q is the principal symbol of Q. Turning the attention to the spectral family {ES}S∈, it is shown that if is considered as a distribution on ×X×X it is in fact a Lagrangian distribution near the set where (s, x, y, σ, ξ,η) are coordinates on T1(×X×X) induced by the coordinates (s, x, y) on ×X×X. This leads to an easy proof that is a pseudodifferential operator if ?∈C∞() and to some results on the microlocal character of Es. Finally, a look at the wavefront set of leads to a conjecture about the existence of absolutely continuous spectrum in terms of a condition on q(x, ξ). 相似文献
20.
A function f(x) defined on = 1 × 2 × … × n where each i is totally ordered satisfying f(x ∨ y) f(x ∧ y) ≥ f(x) f(y), where the lattice operations ∨ and ∧ refer to the usual ordering on , is said to be multivariate totally positive of order 2 (MTP2). A random vector Z = (Z1, Z2,…, Zn) of n-real components is MTP2 if its density is MTP2. Classes of examples include independent random variables, absolute value multinormal whose covariance matrix Σ satisfies ?DΣ?1D with nonnegative off-diagonal elements for some diagonal matrix D, characteristic roots of random Wishart matrices, multivariate logistic, gamma and F distributions, and others. Composition and marginal operations preserve the MTP2 properties. The MTP2 property facilitate the characterization of bounds for confidence sets, the calculation of coverage probabilities, securing estimates of multivariate ranking, in establishing a hierarchy of correlation inequalities, and in studying monotone Markov processes. Extensions on the theory of MTP2 kernels are presented and amplified by a wide variety of applications. 相似文献