共查询到20条相似文献,搜索用时 515 毫秒
1.
We present some techniques in c.c.c. forcing, and apply them to prove consistency results concerning the isomorphism and embeddability relations on the family of ?1-dense sets of real numbers. In this direction we continue the work of Baumgartner [2] who proved the axiom BA stating that every two ?1-dense subsets of are isomorphic, is consistent. We e.g. prove Con(BA+(2?0>?2)). Let <KH,<> be the set of order types of ?1-dense homogeneous subsets of with the relation of embeddability. We prove that for every finite model <L, <->: Con(MA+ <KH, <-> ? <L, <->) iff L is a distributive lattice. We prove that it is consistent that the Magidor-Malitz language is not countably compact. We deal with the consistency of certain topological partition theorems. E.g. We prove that MA is consistent with the axiom OCA which says: “If X is a second countable space of power ?1, and {U0,\h.;,Un?1} is a cover of D(X)XxX-}<x,x>¦x?X} consisting of symmetric open sets, then X can be partitioned into {Xi \brvbar; i ? ω} such that for every i ? ω there is l<n such that D(Xi)?Ul”. We also prove that MA+OCA [xrArr] 2 ?0 = ?2. 相似文献
2.
A.P. Kombarov 《Moscow University Mathematics Bulletin》2017,72(5):203-205
A topological space is said to be paranormal if every countable discrete collection of closed sets {D n : n < ω} can be expanded to a locally finite collection of open sets {U n : n < ω}, i.e., D n ? U n and D m ∩ U n ≠ 0 if and only if D m = D n . It is proved that if F: Comp → Comp is a normal functor of degree ≥ 3 and the compact space F(X) is hereditarily paranormal, then the compact space X is metrizable. 相似文献
3.
The following results are obtained.
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- An open neighbornet U of X has a closed discrete kernel if X has an almost thick cover by countably U-close sets.
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- Every hereditarily thickly covered space is aD and linearly D.
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- Every t-metrizable space is a D-space.
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- X is a D-space if X has a cover {Xα:α<λ} by D-subspaces such that, for each β<λ, the set ?{Xα:α<β} is closed.
4.
For any ordinal λ of uncountable cofinality, a λ-tree is a tree T of height λ such that |T α| < cf(λ) for each α < λ, where T α = {x ∈ T: ht(x) = α}. In this note we get a Pressing Down Lemma for λ-trees and discuss some of its applications. We show that if η is an uncountable ordinal and T is a Hausdorff tree of height η such that |T α | ? ω for each α < η, then the tree T is collectionwise Hausdorff if and only if for each antichain C ? T and for each limit ordinal α ? η with cf(α) > ω, {ht(c): c ∈ C} ∩ α is not stationary in α. In the last part of this note, we investigate some properties of κ-trees, κ-Suslin trees and almost κ-Suslin trees, where κ is an uncountable regular cardinal. 相似文献
5.
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
6.
E. G. Goluzina 《Journal of Mathematical Sciences》1987,38(4):2061-2064
LetP κ,n (λ,β) be the class of functions \(g(z) = 1 + \sum\nolimits_{v = n}^\infty {c_\gamma z^v }\) , regular in ¦z¦<1 and satisfying the condition $$\int_0^{2\pi } {\left| {\operatorname{Re} \left[ {e^{i\lambda } g(z) - \beta \cos \lambda } \right]} \right|} /\left( {1 - \beta } \right)\cos \lambda \left| {d\theta \leqslant \kappa \pi ,} \right.z = re^{i\theta } ,$$ , 0 < r < 1 (κ?2,n?1, 0?Β<1, -π<λ<π/2;M κ,n (λ,β,α),n?2, is the class of functions \(f(z) = z + \sum\nolimits_{v = n}^\infty {a_v z^v }\) , regular in¦z¦<1 and such thatF α(z)∈P κ,n?1(λ,β), where \(F_\alpha (z) = (1 - \alpha )\frac{{zf'(z)}}{{f(z)}} + \alpha (1 + \frac{{zf'(z)}}{{f'(z)}})\) (0?α?1). Onr considers the problem regarding the range of the system {g (v?1)(z?)/(v?1)!}, ?=1,2,...,m,v=1,2,...,N ?, on the classP κ,1(λ,β). On the classesP κ,n (λ,β),M κ,n (λ,β,α) one finds the ranges of Cv, v?n, am, n?m?2n-2, and ofg(?),F ?(?), 0<¦ξ¦<1, ξ is fixed. 相似文献
7.
Jian Li 《Topology and its Applications》2011,158(16):2221-2231
Let (X,T) be a topological dynamical system and F be a Furstenberg family (a collection of subsets of Z+ with hereditary upward property). A point x∈X is called an F-transitive one if {n∈Z+:Tnx∈U}∈F for every non-empty open subset U of X; the system (X,T) is called F-point transitive if there exists some F-transitive point. In this paper, we aim to classify transitive systems by F-point transitivity. Among other things, it is shown that (X,T) is a weakly mixing E-system (resp. weakly mixing M-system, HY-system) if and only if it is {D-sets}-point transitive (resp. {central sets}-point transitive, {weakly thick sets}-point transitive).It is shown that every weakly mixing system is Fip-point transitive, while we construct an Fip-point transitive system which is not weakly mixing. As applications, we show that every transitive system with dense small periodic sets is disjoint from every totally minimal system and a system is Δ?(Fwt)-transitive if and only if it is weakly disjoint from every P-system. 相似文献
8.
M.R. Koushesh 《Topology and its Applications》2007,154(3):698-721
For a non-compact metrizable space X, let E(X) be the set of all one-point metrizable extensions of X, and when X is locally compact, let EK(X) denote the set of all locally compact elements of E(X) and be the order-anti-isomorphism (onto its image) defined in [M. Henriksen, L. Janos, R.G. Woods, Properties of one-point completions of a non-compact metrizable space, Comment. Math. Univ. Carolin. 46 (2005) 105-123; in short HJW]. By definition λ(Y)=?n<ωclβX(Un∩X)\X, where Y=X∪{p}∈E(X) and {Un}n<ω is an open base at p in Y. We characterize the elements of the image of λ as exactly those non-empty zero-sets of βX which miss X, and the elements of the image of EK(X) under λ, as those which are moreover clopen in βX\X. This answers a question of [HJW]. We then study the relation between E(X) and EK(X) and their order structures, and introduce a subset ES(X) of E(X). We conclude with some theorems on the cardinality of the sets E(X) and EK(X), and some open questions. 相似文献
9.
Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces 总被引:1,自引:0,他引:1
Giuseppe Marino 《Journal of Mathematical Analysis and Applications》2007,329(1):336-346
Let C be a closed convex subset of a real Hilbert space H and assume that T is a κ-strict pseudo-contraction on C with a fixed point, for some 0?κ<1. Given an initial guess x0∈C and given also a real sequence {αn} in (0,1). The Mann's algorithm generates a sequence {xn} by the formula: xn+1=αnxn+(1−αn)Txn, n?0. It is proved that if the control sequence {αn} is chosen so that κ<αn<1 and , then {xn} converges weakly to a fixed point of T. However this convergence is in general not strong. We then modify Mann's algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence. This result extends a recent result of Nakajo and Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379] from nonexpansive mappings to strict pseudo-contractions. 相似文献
10.
J.W Moon 《Journal of Combinatorial Theory, Series A》1980,28(1):98-102
If α = {α0, α1,…, αn} and β = {β0, β1,…, βn} are two non-decreasing sets of integers such that α0 = 0 < β0, αn < βn = n, and αi < i < βi for 1 ? i ? n ? 1, let L denote the set of lattice points (p, q) such that 0 ? p ? n and αp ? q ? βp. We determine all such regions L with the property that the number of lattice paths from (0, 0) to (p, p) in L is the Catalan number for 0 ? p ? n. 相似文献
11.
S. Thianwan 《Mathematical Notes》2011,89(3-4):397-407
Let X be a real uniformly convex Banach space and C a nonempty closed convex nonexpansive retract of X with P as a nonexpansive retraction. Let T 1, T 2: C → X be two uniformly L-Lipschitzian, generalized asymptotically quasi-nonexpansive non-self-mappings of C satisfying condition A′ with sequences {k n (i) } and {δ n (i) } ? [1, ∞),, i = 1, 2, respectively such that Σ n=1 ∞ (k n (i) ? 1) < ∞, Σ n=1 (i) δ n (i) < ∞, and F = F(T 1) ∩ F(T 2) ≠ ?. For an arbitrary x 1 ∈ C, let {x n } be the sequence in C defined by $$ \begin{gathered} y_n = P\left( {\left( {1 - \beta _n - \gamma _n } \right)x_n + \beta _n T_2 \left( {PT_2 } \right)^{n - 1} x_n + \gamma _n v_n } \right), \hfill \\ x_{n + 1} = P\left( {\left( {1 - \alpha _n - \lambda _n } \right)y_n + \alpha _n T_1 \left( {PT_1 } \right)^{n - 1} x_n + \lambda _n u_n } \right), n \geqslant 1, \hfill \\ \end{gathered} $$ where {α n }, {β n }, {γ n } and {λ n } are appropriate real sequences in [0, 1) such that Σ n=1 ∞ ] γ n < ∞, Σ n=1 ∞ λ n < ∞, and {u n }, }v n } are bounded sequences in C. Then {x n } and {y n } converge strongly to a common fixed point of T 1 and T 2 under suitable conditions. 相似文献
12.
Let X be a topological space and let F be a filter on N, recall that a sequence (xn)n∈N in X is said to be F-convergent to the point x∈X, if for each neighborhood U of x, {n∈N:xn∈U}∈F. By using F-convergence in ?1 and in Banach spaces, we characterize the P-filters, the P-filters+, the weak P-filters, the Q-filters, the Q-filters+, the weak Q-filters, the selective filters and the selective+ filters. 相似文献
13.
V. A. Zapol’skii 《Journal of Mathematical Sciences》2009,161(3):375-383
A cover of a manifold X is called an r-cover if any r points of X belong to a set in the cover. Let X and Y be two smooth manifolds, let Emb(X, Y) be the family of smooth embeddings X → Y, let M be an Abelian group, and let F: Emb(X, Y) → M be a functional. One says that the degree of F does not exceed r if for each finite open r-cover {U
i
}
i∈I
; of X there exist functionals F
i
: Emb(U
i
, Y) → M, i ∈ I, such that for each a ∈ Emb(X, Y) one has
F(a) = ?i ? I Fi( a| Ui ) F(a) = \sum\limits_{i \in I} {{F_i}\left( {a\left| {_{U_i}} \right.} \right)} 相似文献
14.
A space X is said to be selectively separable (=M-separable) if for each sequence {Dn:n∈ω} of dense subsets of X, there are finite sets Fn⊂Dn (n∈ω) such that ?{Fn:n∈ω} is dense in X. On selective separability and its variations, we show the following: (1) Selective separability, R-separability and GN-separability are preserved under finite unions; (2) Assuming CH (the continuum hypothesis), there is a countable regular maximal R-separable space X such that X2 is not selectively separable; (3) c{0,1} has a selectively separable, countable and dense subset S such that the group generated by S is not selectively separable. These answer some questions posed in Bella et al. (2008) [7]. 相似文献
15.
W.W. Comfort 《Topology and its Applications》2010,157(5):839-856
The recent literature offers examples, specific and hand-crafted, of Tychonoff spaces (in ZFC) which respond negatively to these questions, due respectively to Ceder and Pearson (1967) [3] and to Comfort and García-Ferreira (2001) [5]: (1) Is every ω-resolvable space maximally resolvable? (2) Is every maximally resolvable space extraresolvable? Now using the method of KID expansion, the authors show that every suitably restricted Tychonoff topological space (X,T) admits a larger Tychonoff topology (that is, an “expansion”) witnessing such failure. Specifically the authors show in ZFC that if (X,T) is a maximally resolvable Tychonoff space with S(X,T)?Δ(X,T)=κ, then (X,T) has Tychonoff expansions U=Ui (1?i?5), with Δ(X,Ui)=Δ(X,T) and S(X,Ui)?Δ(X,Ui), such that (X,Ui) is: (i=1) ω-resolvable but not maximally resolvable; (i=2) [if κ′ is regular, with S(X,T)?κ′?κ] τ-resolvable for all τ<κ′, but not κ′-resolvable; (i=3) maximally resolvable, but not extraresolvable; (i=4) extraresolvable, but not maximally resolvable; (i=5) maximally resolvable and extraresolvable, but not strongly extraresolvable. 相似文献
16.
For fixed p (0 ≤ p ≤ 1), let {L0, R0} = {0, 1} and X1 be a uniform random variable over {L0, R0}. With probability p let {L1, R1} = {L0, X1} or = {X1, R0} according as ; with probability 1 ? p let {L1, R1} = {X1, R0} or = {L0, X1} according as , and let X2 be a uniform random variable over {L1, R1}. For n ≥ 2, with probability p let {Ln, Rn} = {Ln ? 1, Xn} or = {Xn, Rn ? 1} according as , with probability 1 ? p let {Ln, Rn} = {Xn, Rn ? 1} or = {Ln ? 1, Xn} according as , and let Xn + 1 be a uniform random variable over {Ln, Rn}. By this iterated procedure, a random sequence {Xn}n ≥ 1 is constructed, and it is easy to see that Xn converges to a random variable Yp (say) almost surely as n → ∞. Then what is the distribution of Yp? It is shown that the Beta, (2, 2) distribution is the distribution of Y1; that is, the probability density function of Y1 is g(y) = 6y(1 ? y) I0,1(y). It is also shown that the distribution of Y0 is not a known distribution but has some interesting properties (convexity and differentiability). 相似文献
17.
LetX 1,X 2,... be a sequence of independent random variables with distributionF. Suppose that 0<p<1, thatξ p is the uniquepth quantile ofF, and thatξ p,n is the samplepth quantile ofX 1,...,X n . Ifb(n)→0+ sufficiently slowly, then $$N(b) = \sum\limits_{n = 1}^\infty {I\left\{ {\left| {\xi _{p,n} - \xi _p } \right| > b(n)} \right\}} $$ and $$L(b) = \sup \left\{ {n:\left| {\xi _{p,n} - \xi _p } \right| > b(n)} \right\}$$ are proper random variables (finite with probability one). In this paper we investigate the moment behavior of exp{Nb 2 (N)} and exp{Lb 2 (L)}. 相似文献
18.
Assuming the absence of Q-points (which is consistent with ZFC) we prove that the free topological group F(X) over a Tychonov space X is o-bounded if and only if every continuous metrizable image T of X satisfies the selection principle fin?(O,Ω) (the latter means that for every sequence 〈un〉n∈ω of open covers of T there exists a sequence 〈vn〉n∈ω such that vn∈[un]<ω and for every F∈[X]<ω there exists n∈ω with F⊂?vn). This characterization gives a consistent answer to a problem posed by C. Hernándes, D. Robbie, and M. Tkachenko in 2000. 相似文献
19.
Let {Xn, n ? 1} be a sequence of identically distributed random variables, Zn = max {X1,…, Xn} and {un, n ? 1 } an increasing sequence of real numbers. Under certain additional requirements, necessary and sufficient conditions are given to have, with probability one, an infinite number of crossings of {Zn} with respect to {un}, in two cases: (1) The Xn's are independent, (2) {Xn} is stationary Gaussian and satisfies a mixing condition. 相似文献
20.
A proof is given for the existence and uniqueness of a correspondence between two pairs of sequences {a},{b} and {ω},{μ}, satisfying bi>0 for i=1,…,n?1 and ω1<μ1<?<μn?1<ωn, under which the symmetric Jacobi matrices J(n,a,b) and J(n?1,a,b) have eigenvalues {ω} and {μ} respectively. Here J(m,a,b) is symmetric and tridiagonal with diagonal elements ai (i=1,…,m) and off diagonal elements bi (i=1,…,m?1). A new concise proof is given for the known uniqueness result. The existence result is new. 相似文献
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