共查询到20条相似文献,搜索用时 78 毫秒
1.
We give an example of a perfectly normal first countable space X1 with ind X1 = 1 such that if Z is a Lindelöf space containing X1. then ind Z=dim Z=∞. Under CH, there is a perfectly normal, hereditarily separable and first countable such space. 相似文献
2.
A. Bouziad 《Topology and its Applications》2007,154(2):287-301
A topological space X is said to have the Scorza-Dragoni property if the following property holds: For every metric space Y and every Radon measure space (T,μ), any Carathéodory function is Luzin measurable, i.e., given ε>0, there is a compact set K in T with μ(T?K)?ε such that the mapping is continuous. We present a selection of spaces without the Scorza-Dragoni property, among which there are first countable hereditarily separable and hereditarily Lindelöf compact spaces, separable Moore spaces and even countable k-spaces. In the positive direction, it is shown that every space which is an ℵ0-space and kR-space has the Scorza-Dragoni property. We also prove that every separately continuous mapping , where Y is a metric space, is Luzin measurable, provided the space X is strongly functionally generated by a countable collection of its bounded subsets. If Martin's Axiom is assumed then all metric spaces of density less than c, and all pseudocompact spaces of cardinality less than c, have the Scorza-Dragoni property with respect to every separable Radon measure μ. Finally, the class of countable spaces with the Scorza-Dragoni property is closely examined. 相似文献
3.
Let Cα(X,Y) be the set of all continuous functions from X to Y endowed with the set-open topology where α is a hereditarily closed, compact network on X which is closed under finite unions. We proved that the density of the space Cα(X,Y) is at most iw(X)⋅d(Y) where iw(X) denotes the i-weight of the Tychonoff space X, and d(Y) denotes the density of the space Y when Y is an equiconnected space with equiconnecting function Ψ, and Y has a base consists of Ψ-convex subsets of Y. We also prove that the equiconnectedness of the space Y cannot be replaced with pathwise connectedness of Y. In fact, it is shown that for each infinite cardinal κ, there is a pathwise connected space Y such that π-weight of Y is κ, but Souslin number of the space Ck([0,1],Y) is κ2. 相似文献
4.
Haruto Ohta 《Topology and its Applications》1984,17(3):265-274
In response to questions of Ginsburg [9, 10], we prove that if cf(c)>ω1, then there exists an open-closed, continuous map f from a normal, realcompact space X onto a space Y which is not realcompact. By his result the hyperspace 2x of closed subsets of X is then not realcompact, and the extension μf(vf) of f to the topological completion (the Hewitt realcompactification) of X is not onto. The latter fact solves problems raised by Morita [16] and by Isiwata [12] both negatively. We also consider the problem whether or not the hyperspace of a hereditarily Lindelöf space is hereditarily realcompact. 相似文献
5.
Michel Smith 《Topology and its Applications》2009,156(3):522-524
We prove that if each of X and Y is a Souslin arc (a Hausdorff arc that is the compactification of a connected Souslin line), then every hereditarily indecomposable subcontinuum of X×Y is metric. 相似文献
6.
Jan van Mill 《Topology and its Applications》1982,13(2):123-132
The reduced measure algebra is used to construct, under CH, a hereditarily Lindelöf separable K1-space X which is not a K0-space. 相似文献
7.
In 1975 Hagopian proved that continua X and Y are atriodic and hereditarily unicoherent when the product X×Y is disk-like. In this paper, under the same condition, we prove that X and Y are contractible with respect to every ANR and X and Y are tree-like continua in ClassHW. 相似文献
8.
The following result, and a closely related one, is proved: If u:X → Y is an open, perfect surjection, with X metrizable and with dim X = 0 or dim Y = 0, then there exists a perfect surjection such that u ° h = πY (where S in the Cantor set and is the projection). If moreover, u-1(y) is homeomorphic to S for all y?Y, then h can be chosen to be a homeomorphism. 相似文献
9.
Eiji Kurihara 《Topology and its Applications》1984,17(1):47-54
It is shown that if dim Y < ∞ and if f(X) = Y is a mapping between compact metric spaces such that 1 ? m ? dim f-1(y)?n for all y ? Y, then there exists a closed set K ? X such that dim K ? n ? m and dim f(K) = dim Y. This answers a question posed by J. Keesling and D. Wilson. 相似文献
10.
Let be a surjection of a zero-dimensional metrizable X onto a metrizable Y which maps clopen sets in X to locally closed (or more generally, resolvable) sets in Y. We prove that if X is completely metrizable, or hereditarily Baire, then Y has also the respective property. This strengthens some recent results of A. Ostrovsky (2009) [5] and provides an answer to his question. 相似文献
11.
We demonstrate that for every n<ω there exists a separable completely metrizable space Xn which has a continuous selection for its Vietoris hyperspace of nonempty compact subsets, but dim(Xn)=n. Related results and open problems are discussed. 相似文献
12.
Liang-Xue Peng 《Topology and its Applications》2012,159(1):304-307
Let μ and ν be two ordinals. If X is a subspace of μ×ν, then X is dually discrete. This gives a positive answer to a question of Alas, Junqueira and Wilson. By this conclusion and a known conclusion we show that a subspace Y of μ×ν has countable spread if and only if the space Y is hereditarily a Lindelöf D-space. 相似文献
13.
Haruto Ohta 《Topology and its Applications》1982,13(2):155-165
We generalize and refine results from the author's paper [18]. For a completely regular Hausdorff space X, υX denotes the Hewitt realcompactification of X. It is proved that if υ(X×Y)=υX×υY for any metacompact subparacompact (or m-paracompact) space Y, then X is locally compact. A P(n)-space is a space in which every intersection of less than n open sets is open. A characterization of those spaces X such that υ (X×Y = υX×υY for any (metacompact) P(n)-space Y is also obtained. 相似文献
14.
A.P. Kombarov 《Topology and its Applications》2010,157(4):694-697
Let X be a Hausdorff topological space and exp(X) be the space of all (nonempty) closed subsets of a space X with the Vietoris topology. We consider hereditary normality-type properties of exp(X). In particular, we prove that if exp(X) is hereditarily D-normal, then X is a metrizable compact space. 相似文献
15.
For a natural number m?0, a map from a compactum X to a metric space Y is an m-dimensional Lelek map if the union of all non-trivial continua contained in the fibers of f is of dimension ?m. In [M. Levin, Certain finite-dimensional maps and their application to hyperspaces, Israel J. Math. 105 (1998) 257-262], Levin proved that in the space C(X,I) of all maps of an n-dimensional compactum X to the unit interval I=[0,1], almost all maps are (n−1)-dimensional Lelek maps. Moreover, he showed that in the space C(X,Ik) of all maps of an n-dimensional compactum X to the k-dimensional cube Ik (k?1), almost all maps are (n−k)-dimensional Lelek maps. In this paper, we generalize Levin's result. For any (separable) metric space Y, we define the piecewise embedding dimension ped(Y) of Y and we prove that in the space C(X,Y) of all maps of an n-dimensional compactum X to a complete metric ANR Y, almost all maps are (n−k)-dimensional Lelek maps, where k=ped(Y). As a corollary, we prove that in the space C(X,Y) of all maps of an n-dimensional compactum X to a Peano curve Y, almost all maps are (n−1)-dimensional Lelek maps and in the space C(X,M) of all maps of an n-dimensional compactum X to a k-dimensional Menger manifold M, almost all maps are (n−k)-dimensional Lelek maps. It is known that k-dimensional Lelek maps are k-dimensional maps for k?0. 相似文献
16.
17.
Petr Holický 《Topology and its Applications》2010,157(12):1926-275
We show that a metrizable space Y is completely metrizable if there is a continuous surjection f:X→Y such that the images of open (clopen) subsets of the (0-dimensional paracompact) ?ech-complete space X are resolvable subsets of Y (in particular, e.g., the elements of the smallest algebra generated by open sets in Y). 相似文献
18.
A.V. Ivanov 《Topology and its Applications》2010,157(3):517-521
We construct, assuming the continuum hypothesis, an example of nonmetrizable n-dimensional Cantor manifold Xn(n∈N) with the following properties: 1) is hereditarily separable for all k∈N; 2) is perfectly normal for every k∈N; 3) the space F(Xn) is hereditarily normal for every seminormal functor F that preserves weights and one-to-one points and such that sp(F)={1,k}; in particular, and λ3Xn are hereditarily normal. This example is a generalization of famous Gruenhage's example given in Gruenhage and Nyikos (1993) [4]. 相似文献
19.
Warren B. Moors 《Topology and its Applications》2007,154(2):428-433
In this paper we prove a theorem more general than the following. Suppose that X is ?ech-complete and Y is a closed subset of a product of a separable metric space with a compact Hausdorff space. Then for each separately continuous function there exists a residual set R in X such that f is jointly continuous at each point of R×Y. This confirms the suspicions of S. Mercourakis and S. Negrepontis from 1991. 相似文献
20.
Stoyan Nedev 《Topology and its Applications》2009,156(7):1234-1240
For every space X let K(X) be the set of all compact subsets of X. Christensen [J.P.R. Christensen, Necessary and sufficient conditions for measurability of certain sets of closed subsets, Math. Ann. 200 (1973) 189-193] proved that if X,Y are separable metrizable spaces and F:K(X)→K(Y) is a monotone map such that any L∈K(Y) is covered by F(K) for some K∈K(X), then Y is complete provided X is complete. It is well known [J. Baars, J. de Groot, J. Pelant, Function spaces of completely metrizable space, Trans. Amer. Math. Soc. 340 (1993) 871-879] that this result is not true for non-separable spaces. In this paper we discuss some additional properties of F which guarantee the validity of Christensen's result for more general spaces. 相似文献