共查询到20条相似文献,搜索用时 31 毫秒
1.
Yukinobu Yajima 《Topology and its Applications》2006,153(17):3220-3229
Stone, Michael and Morita have given various equivalent conditions for normal covers of topological spaces. Here, as an analogue of the classic characterization, we give some characterizations for normal covers of rectangular products in terms of cozero rectangles. Moreover, we apply our characterizations to consider the base-paracompactness of rectangular products. 相似文献
2.
Yukinobu Yajima 《Topology and its Applications》2010,157(8):1569-1592
Throughout this paper, we consider the following two problems: (A) When does a rectangular normal cover of a product X×Y (or an infinite product ∏λ∈ΛXλ) have a σ-locally finite rectangular cozero refinement? (B) What kind of a refinement makes a rectangular open cover of a product X×Y (or an infinite product ∏λ∈ΛXλ) be normal? We shall discuss these problems on various products listed below. 相似文献
3.
Nobuyuki Kemoto 《Topology and its Applications》2007,154(3):758-770
Let A and B be subspaces of an ordinal. It is proved that the product A×B is countably paracompact if and only if it is rectangular. Before this main result, we discuss several covering properties of products with one ordinal factor. In particular, for every paracompact space X, it is proved that the product X×A is paracompact if so is A. 相似文献
4.
Several results on rectangular products in the sense of B.A. Pasynkov will be obtained, one of which asserts that for a Tychonoff space X, X × Y is rectangular for any space Y iff X is locally compact and paracompact. 相似文献
5.
We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of symmetric blocks of independent Hermitian random matrices which are asymptotically free, asymptotically free from diagonal deterministic matrices, and whose norms are uniformly bounded almost surely. This class contains symmetric blocks of unitarily invariant Hermitian random matrices whose asymptotic distributions are compactly supported probability measures on the real line. Our approach is based on the concept of matricial freeness which is a generalization of freeness in free probability. We show that the associated matricially free Gaussian operators provide a unified framework for studying the limit distributions of sums and products of independent rectangular random matrices, including non-Hermitian Gaussian matrices and matrices of Wishart type. 相似文献
6.
Yukinobu Yajima 《Topology and its Applications》2012,159(4):1223-1235
Recently, it has been proved that orthocompactness implies normality for the products of a monotonically normal space and a compact space. It had been known that normality, collectionwise normality and the shrinking property are equivalent for the same products. We extend these two results for the products replacing the compact factor with a factor defined by topological games. Moreover, we prove the equivalence of orthocompactness and weak suborthocompactness in these products. 相似文献
7.
We prove that any product of quotient maps in the category of quasi-uniform spaces and quasi-uniformly continuous maps is a quotient map. We also show that a quasi-uniformly continuous map from a product of quasi-uniform spaces into a quasi-pseudometric T0-space depends on countably many coordinates.Furthermore we characterize those quasi-uniformities that are unique in their quasi-proximity class and prove that this property is preserved under arbitrary products in the category of quasi-uniform spaces. 相似文献
8.
We characterize the functions which are infinite products of quasi-continuous functions. We show in particular that each cliquish function is such a product, and we conclude that the Π-classification generated by the family stabilizes from the second class on. 相似文献
9.
《Quaestiones Mathematicae》2013,36(1-3):191-205
Abstract Examples are provided which demonstrate that in many cases topological products do not behave as they should. A new product for topological spaces is defined in a natural way by means of interior covers. In general this is no longer a topological space but can be interpreted as categorical product in a category larger than Top. For compact spaces the new product coincides with the old. There is a converse: For symmetric topological spaces X the following conditions are equivalent: (1) X is compact; (2) for each cardinal k the old and the new product Xk coincide; (3) for each compact Hausdorff space Y the old and the new product X x Y coincide. The new product preserves paracompactness, zero-dimensionality (in the covering sense), the Lindelöf property, and regular-closedness. With respect to the new product, a space is N-complete iff it is zerodimensional and R-complete. 相似文献
10.
Alessandro Berarducci Dikran Dikranjan Jan Pelant 《Topology and its Applications》2009,156(7):1422-1437
A metric space X is straight if for each finite cover of X by closed sets, and for each real valued function f on X, if f is uniformly continuous on each set of the cover, then f is uniformly continuous on the whole of X. A locally connected space is straight iff it is uniformly locally connected (ULC). It is easily seen that ULC spaces are stable under finite products. On the other hand the product of two straight spaces is not necessarily straight. We prove that the product X×Y of two metric spaces is straight if and only if both X and Y are straight and one of the following conditions holds:
- (a)
- both X and Y are precompact;
- (b)
- both X and Y are locally connected;
- (c)
- one of the spaces is both precompact and locally connected.
11.
Yukinobu Yajima 《Topology and its Applications》2007,154(1):103-114
We give some characterizations for normal covers of infinite products of generalized metric spaces such as M-spaces, Σ-spaces and β-spaces. We prove them simultaneously in terms of β-spaces and perfect maps. Next, we give affirmative answers to two questions concerning the normality of Σ-products, which were raised by the author and Yamazaki, respectively. These results are stated in terms of Σ-products of β-spaces. 相似文献
12.
Désirée Basile 《Topology and its Applications》2008,155(4):180-189
In [A.V. Arhangel'ski?, Remainders in compactifications and generalized metrizability properties, Topology Appl. 150 (2005) 79-90], Arhangel'ski? introduced the notion of Ohio completeness and proved it to be a useful concept in his study of remainders of compactifications and generalized metrizability properties. We will investigate the behavior of Ohio completeness with respect to closed subspaces and products. We will prove among other things that if an uncountable product is Ohio complete, then all but countably many factors are compact. As a consequence, Rκ is not Ohio complete, for every uncountable cardinal number κ. 相似文献
13.
Dikran Dikranjan 《Topology and its Applications》2007,154(7):1321-1340
We study CLP-compact spaces (every cover consisting of clopen sets has a finite subcover) and CLP-compact topological groups. In particular, we extend a theorem on CLP-compactness of products from [J. Steprāns, A. Šostak, Restricted compactness properties and their preservation under products, Topology Appl. 101 (3) (2000) 213-229] and we offer various criteria for CLP-compactness for spaces and topological groups, that work particularly well for precompact groups. This allows us to show that arbitrary products of CLP-compact pseudocompact groups are CLP-compact. For every natural n we construct:
- (i)
- a totally disconnected, n-dimensional, pseudocompact CLP-compact group; and
- (ii)
- a hereditarily disconnected, n-dimensional, totally minimal, CLP-compact group that can be chosen to be either separable metrizable or pseudocompact (a Hausdorff group G is totally minimal when all continuous surjective homomorphisms G→H, with a Hausdorff group H, are open).
14.
Eva Murtinová 《Topology and its Applications》2006,153(18):3402-3408
Assuming a measurable cardinal exists, we construct a pair of discretely generated spaces whose product fails to be weakly discretely generated. Under the Continuum Hypothesis, a similar result is obtained for a pair of countable Fréchet spaces as well as for two compact discretely generated spaces whose product is not discretely generated. A somewhat weaker example is presented assuming Martin's Axiom for countable posets. Further, the class of strongly discretely generated compacta is shown to preserve discrete generability in products. 相似文献
15.
Francis Jordan 《Topology and its Applications》2007,154(4):870-883
We characterize the spaces X for which the space Cp(X) of real valued continuous functions with the topology of pointwise convergence has local properties related to the preservation of countable tightness or the Fréchet property in products. In particular, we use the methods developed to construct an uncountable subset W of the real line such that the product of Cp(W) with any strongly Fréchet space is Fréchet. The example resolves an open question. 相似文献
16.
We prove that every scattered space is hereditarily subcompact and any finite union of subcompact spaces is subcompact. It is a long-standing open problem whether every ?ech-complete space is subcompact. Moreover, it is not even known whether the complement of every countable subset of a compact space is subcompact. We prove that this is the case for linearly ordered compact spaces as well as for ω -monolithic compact spaces. We also establish a general result for Tychonoff products of discrete spaces which implies that dense Gδ-subsets of Cantor cubes are subcompact. 相似文献
17.
Gino Tironi 《Mediterranean Journal of Mathematics》2006,3(2):313-325
In this paper it is given a survey of principal results (old and new) concerning the class of pseudoradial spaces. In this
class cardinal invariants and their inequalities are considered. The behaviour of pseudoradial spaces under the operations
of taking topological products and subspaces are examined and a typical proof is given. A particular attention is dedicated
to the so called “small cardinals” in connection with pseudoradiality. Pseudoradiality of 2ω 2 is also examined. It is proved that pseudoradiality can be ω1 productive for spaces of weight at most ω2. Finally, several open problems are presented.
This work was supported by the National Group “Real Analysis, Measure Theory with Applications to Economy” of the Italian
Ministery of Education, University and Research. 相似文献
18.
19.
Fernando Hernández-Hernández Paul J. Szeptycki Artur H. Tomita 《Topology and its Applications》2007,154(16):2997-3004
We study realcompactness in the classes of submaximal and maximal spaces. It is shown that a normal submaximal space of cardinality less than the first measurable is realcompact. ZFC examples of submaximal not realcompact and maximal not realcompact spaces are constructed. These examples answer questions posed in [O.T. Alas, M. Sanchis, M.G. Tka?enko, V.V. Tkachuk, R.G. Wilson, Irresolvable and submaximal spaces: homogeneity versus σ-discreteness and new ZFC examples, Topology Appl. 107 (3) (2000) 259-273] and generalize some results from [D.P. Baturov, On perfectly normal dense subspaces of products, Topology Appl. 154 (2) (2007) 374-383]. 相似文献
20.
Problems of inserting lattice-valued functions are investigated. We provide an analogue of the classical insertion theorem of Lane [Proc. Amer. Math. Soc. 49 (1975) 90-94] for L-valued functions where L is a ?-separable completely distributive lattice (i.e. L admits a countable join-dense subset which is free of completely join-irreducible elements). As a corollary we get an L-version of the Katětov-Tong insertion theorem due to Liu and Luo [Topology Appl. 45 (1992) 173-188] (our proof is different and much simpler). We show that ?-separable completely distributive lattices are closed under the formation of countable products. In particular, the Hilbert cube is a ?-separable completely distributive lattice and some join-dense subset is shown to be both order and topologically isomorphic to the hedgehog J(ω) with appropriately defined topology. This done, we deduce an insertion theorem for J(ω)-valued functions which is independent of that of Blair and Swardson [Indian J. Math. 29 (1987) 229-250]. Also, we provide an iff criterion for inserting a pair of semicontinuous function which yields, among others, a characterization of hereditarily normal spaces. 相似文献