共查询到20条相似文献,搜索用时 93 毫秒
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在文献[1]中,R.M.Stepheson.Jr.提出问题:是否每一个局部弱紧的,第一可数的正则的空间都存在一个第一可数的正则的一闭扩充?在此文中,我们给出了一个非弱紧而局部弱紧空间 X 具有形状为 X ∪{∞}的,第一可数的正则一闭扩充的充分必要条件,同时得到了两个有趣的推论。 相似文献
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刘来山 《高校应用数学学报(A辑)》2012,27(3)
给出一个弱拟第一可数空间成为弱第一可数空间的充要条件,证明了空间是弱第一可数空间当且仅当它是具有序列点Gδ性质的弱拟第一可数空间且不含Sw的闭拷贝.同时还证明了每一弱第一可数空间(弱拟第一可数空间)都是某个第一可数空间的商二到一映像(商可数到一映像),作为应用,部分回答了林寿(2007)的一个问题. 相似文献
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讨论了Lasnev空间的超空间的某些性质.文中构造一反例,证明存在可数Lasnev空间,其紧子集超空间不是层型空间.并指出文[6]中关于上述结果的证明中有一关键性失误,故[6]中的反例尚不能说明上述结论成立.本文还对具有σ-CF拟基的k′空间给出一个刻画定理 相似文献
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局部可数集族、局部有限集族与Alexandroff问题 总被引:9,自引:0,他引:9
本文引进分层强s-映射和分层强紧映射建立具有σ-局部可数网、具有σ-局部可数k-网、具有σ-局部可数基的正则空间以及σ-空间、-空间、g-可度量空间和确定的度量空间之间的联系.这些都是对Alexandroff问题的回答. 相似文献
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局部可数集族、局部有限集族与Alexandroff问题 总被引:6,自引:1,他引:5
本文引进分层强s-映射和分层强紧映射建立具有σ-局部可数网、具有σ-局部可数k-网、具有σ-局部可数基的正则空间以及σ-空间、-空间、g-可度量空间和确定的度量空间之间的联系.这些都是对Alexandroff问题的回答. 相似文献
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一类g-第一可数空间的刻画 总被引:7,自引:1,他引:6
本文引进了弱开映射,利用它把一类g-第一可数空间刻画为度量空间在不同弱开映射下的象,特别地,本文肯定回答了Hoshina的一个问题。 相似文献
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Lajos Soukup 《Topology and its Applications》2008,155(4):347-353
Nagata conjectured that every M-space is homeomorphic to a closed subspace of the product of a countably compact space and a metric space. Although this conjecture was refuted by Burke and van Douwen, and A. Kato, independently, but we can show that there is a c.c.c. poset P of size ω2 such that in VP Nagata's conjecture holds for each first countable regular space from the ground model (i.e. if a first countable regular space X∈V is an M-space in VP then it is homeomorphic to a closed subspace of the product of a countably compact space and a metric space in VP). By a result of Morita, it is enough to show that every first countable regular space from the ground model has a first countable countably compact extension in VP. As a corollary, we also obtain that every first countable regular space from the ground model has a maximal first countable extension in model VP. 相似文献
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A. S. Kechris 《Journal of Mathematical Sciences》2007,140(3):398-425
We call a measure-preserving action of a countable discrete group on a standard probability space tempered if the associated
Koopman representation restricted to the orthogonal complement to the constant functions is weakly contained in the regular
representation. Extending a result of Hjorth, we show that every tempered action is antimodular, i.e., in a precise sense
“orthogonal” to any Borel action of a countable group by automorphisms on a countable rooted tree. We also study tempered
actions of countable groups by automorphisms on compact metrizable groups, where it turns out that this notion has several
ergodic theoretic reformulations and fits naturally in a hierarchy of strong ergodicity properties strictly between ergodicity
and strong mixing. Bibliography:s 25 titles.
Dedicated to Professor Anatoly Vershik on the occasion of his 70th birthday
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 97–144. 相似文献
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彭良雪 《数学物理学报(A辑)》2006,26(5):653-658
人们知道每个C-似空间是 D -空间, 且每个正则弱θ -可加细 C-散布空间也是D -空间。上述空间类的积空间还是D -空间吗?在这篇文章中作者讨论了该问题, 得到如下结论:正则弱θ -可加细空间的有限积是D -空间; 正则Lindel\"of C-散布空间的可数积是D -空间 相似文献
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Yan-Kui Song 《Central European Journal of Mathematics》2013,11(10):1755-1762
We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed subspace which is not star countable (hence not absolutely star countable); (4) assuming $2^{\aleph _0 } = 2^{\aleph _1 }$ , there exists an absolutely star countable normal space having a regular closed subspace which is not star countable (hence not absolutely star countable). 相似文献
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We show in a direct way that a space is D if it is a finite union of subparacompact scattered spaces. This result cannot be extended to countable unions, since it is known that there is a regular space which is a countable union of paracompact scattered spaces and which is not D. Nevertheless, we show that every space which is the union of countably many regular Lindelöf C-scattered spaces has the D-property. Also, we prove that a space is D if it is a locally finite union of regular Lindelöf C-scattered spaces. 相似文献
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A structure is called weakly oligomorphic if its endomorphism monoid has only finitely many invariant relations of every arity. The goal of this paper is to show that the notions of homomorphism‐homogeneity, and weak oligomorphy are not only completely analogous to the classical notions of homogeneity and oligomorphy, but are actually closely related. We first prove a Fraïssé‐type theorem for homomorphism‐homogeneous relational structures. We then show that the countable models of the theories of countable weakly oligomorphic structures are mutually homomorphism‐equivalent (we call first order theories with this property weakly ω‐categorical). Furthermore we show that every weakly oligomorphic homomorphism‐homogeneous structure contains (up to isomorphism) a unique homogeneous, homomorphism‐homogeneous core, to which it is homomorphism‐equivalent. As a consequence we obtain that every countable weakly oligomorphic structure is homomorphism‐equivalent to a finite or ω‐categorical structure. As a corollary we obtain a characterization of positive existential theories of weakly oligomorphic structures as the positive existential parts of ω‐categorical theories. 相似文献
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某些局部凸空间上相对弱紧集,相对弱列紧集,相对弱可数紧集的关系 总被引:3,自引:0,他引:3
对可分离的局部凸空间(X,τ),本文建立了相应的局部凸空间(Qx,Tx),利用它证明了当(X,τ)满足某些条件时(赋范空间满足这些条件),EX相对弱紧E相对弱列紧E相对弱可数紧,从而推广了Eberlein等人的工作,证明了在空间D(R ̄n),(R ̄n)和D_(LP),1<p<∞上前述三种弱紧性等价. 相似文献
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A. Bouziad 《Topology and its Applications》2002,120(3):805-299
For a Hausdorff space X, let F be the hyperspace of all closed subsets of X and H a sublattice of F. Following Nogura and Shakhmatov, X is said to be H-trivial if the upper Kuratowski topology and the co-compact topology coincide on H. F-trivial spaces are the consonant spaces first introduced and studied by Dolecki, Greco and Lechicki. In this paper, we deal with K-trivial spaces and Fin-trivial space, where K and Fin are respectively the lattices of compact and of finite subsets of X. It is proved that if Ck(X) is a Baire space or more generally if X has ‘the moving off property’ of Gruenhage and Ma, then X is K-trivial. If X is countable, then Cp(X) is Baire if and only if X is Fin-trivial and all compact subsets of X are finite. As for consonant spaces, it turns out that every regular K-trivial space is a Prohorov space. This result remains true for any regular Fin-trivial space in which all compact subsets are scattered. It follows that every regular first countable space without isolated points, all compact subsets of which are countable, is Fin-nontrivial. Examples of K-trivial non-consonant spaces, of Fin-trivial K-nontrivial spaces and of countably compact Prohorov Fin-nontrivial spaces, are given. In particular, we show that all (generalized) Fréchet–Urysohn fans are K-trivial, answering a question by Nogura and Shakhmatov. Finally, we describe an example of a continuous open compact-covering mapping f :X→Y, where X is Prohorov and Y is not Prohorov, answering a long-standing question by Topsøe. 相似文献
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Weakly n-dimensional spaces were first distinguished by Karl Menger. In this note we shall discuss three topics concerning this class of spaces: universal spaces, products, and the sum theorem. We prove that there is a universal space for the class of all weakly n-dimensional spaces, present a simpler proof of Tomaszewski’s result about the dimension of a product of weakly n-dimensional spaces, and show that there is an n-dimensional space which admits a pairwise disjoint countable closed cover by weakly n-dimensional subspaces but is not weakly n-dimensional itself. 相似文献