共查询到20条相似文献,搜索用时 31 毫秒
1.
Jan van Mill 《Topology and its Applications》1981,12(3):315-320
There is an AR X and a non-AR Y and a continuous surjection f:X→Y so that each point-inverse f-1(y) is an AR. This solves a problem of Borsuk. 相似文献
2.
R.A. McCoy 《Topology and its Applications》1980,11(2):189-197
A study is made of the natural function which maps each point x of a space X to the evaluation function ex:Yx→Y defined by . A consequence of the results is that βX and υX can both be considered as subspaces of spaces of continous functions from appropriate domain spaces into I or R, respectively. 相似文献
3.
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
4.
Kôichi Tsuda 《Topology and its Applications》1985,20(2):191-200
The following example is constructed without any set-theoretic assumptions beyond ZFC: There exist a hereditarily separable hereditarily Lindelöf space X and a first-countable locally compact separable pseudocompact space Y such that dim X = dimY = 0, while dim(X × Y)>0. 相似文献
5.
Siegfried Graf 《Topology and its Applications》1981,12(3):247-256
The complete Boolean homomorphisms from the category algebra (X) of a complete matrix space X to the category algebra (Y) of a Baire topological space Y are characterized as those σ-homomorphisms which are induced by continuous maps from dense G8-subsets of Y into X. This result is used to deduce a series of related results in topology and measure theory (some of which are well-known). Finally a similar result for the complete Boolean homomorphisms from the category algebra (X) of a compact Hausdorff space X tothe category algebra (Y) of a Baire topological space Y is proved. 相似文献
6.
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
7.
Vesko Valov 《Topology and its Applications》2008,155(8):906-915
It is shown that if is a perfect map between metrizable spaces and Y is a C-space, then the function space C(X,I) with the source limitation topology contains a dense Gδ-subset of maps g such that every restriction map gy=g|f−1(y), y∈Y, satisfies the following condition: all fibers of gy are hereditarily indecomposable and any continuum in f−1(y) either contains a component of a fiber of gy or is contained in a fiber of gy. 相似文献
8.
It is shown that every Euclidean manifold M has the following property for any m?1: If f:X→Y is a perfect surjection between finite-dimensional metric spaces, then the mapping space C(X,M) with the source limitation topology contains a dense Gδ-subset of maps g such that dimBm(g)?mdimf+dimY−(m−1)dimM. Here, Bm(g)={(y,z)∈Y×M||f−1(y)∩g−1(z)|?m}. The existence of residual sets of finite-to-one maps into product of manifolds and spaces having disjoint disks properties is also obtained. 相似文献
9.
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
10.
S. Purisch 《Topology and its Applications》1983,16(3):273-277
Let X be a nonarchimedean space and C be the union of all compact open subsets of X. The following conditions are listed in increasing order of generality. (Conditions 2 and 3 are equivalent.) 1. X is perfect; 2. C is an Fσ in X; 3. C? is metrizable; 4. X is orderable. It is also shown that X is orderable if is scattered or X is a GO space with countably many pseudogaps. An example is given of a non-orderable, totally disconnected, GO space with just one pseudogap. 相似文献
11.
A weak selection on an infinite set X is a function σ:[X]2→X such that σ({x,y})∈{x,y} for each {x,y}∈[X]2. A weak selection on a space is said to be continuous if it is a continuous function with respect to the Vietoris topology on [X]2 and the topology on X . We study some topological consequences from the existence of a continuous weak selection on the product X×Y for the following particular cases:
- (i)
- Both X and Y are spaces with one non-isolated point. 相似文献
12.
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
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.
Fons van Engelen 《Topology and its Applications》1984,17(3):275-285
Let X be separable, completely metrizable, and dense in itself. We show that if X admits a triple (D1, D2, h) of two countable dense subsets D1 and D2 and a homeomorphism h: X?D1 → X?D2, satisfying some special properties, then there is a rigid subspace A of X such that A is homeomorphic to X?A = h[A]; for , such atriple is shown to exist. 相似文献
15.
Kevin Bicknell 《Topology and its Applications》1980,11(2):111-119
The set of continuous-from-the-right step functions from the half-open unit interval[0, 1[into a topological space X is denoted by X1. Elsewhere a topology has been defined which makes X1 a contractible, locally contractible space with the subspace of constant functions being homeomorphic to X. When X has a bounded metric ?, the topology of X1 may be described by the metric .It is shown here that if X is separable, then X1 is separable and if X satisfies the first (or second) axiom of countability, then X1 satisfies it too. In contrast, it is shown that properties such as normality do not extend from X to X1. This follows from the main result: X1 is homeomorphic to its square, and thus contains a copy of X×X (which is closed when X is Hausdorff). The final theorem states that if X has at least two points then X1 is not complete metrizable. 相似文献
16.
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
17.
For a Whitney preserving map f:X→G we show the following: (a) If X is arcwise connected and G is a graph which is not a simple closed curve, then f is a homeomorphism; (b) If X is locally connected and G is a simple closed curve, then X is homeomorphic to either the unit interval [0,1], or the unit circle S1. As a consequence of these results, we characterize all Whitney preserving maps between finite graphs. We also show that every hereditarily weakly confluent Whitney preserving map between locally connected continua is a homeomorphism. 相似文献
18.
R.A. Maller 《Stochastic Processes and their Applications》1978,8(2):171-179
Let Xi be iidrv's and Sn=X1+X2+…+Xn. When EX21<+∞, by the law of the iterated logarithm for some constants αn. Thus the r.v. is a.s.finite when δ>0. We prove a rate of convergence theorem related to the classical results of Baum and Katz, and apply it to show, without the prior assumption EX21<+∞ that EYh<+∞ if and only if for 0<h<1 and δ> , whereas whenever h>0 and . 相似文献
19.
A compactificaton αX of a completely regular space X is “determined” by a subset F of C1(X) if αX is the smallest compactificaton of X to which each element of F extends, and is “generated” by F if the evaluation map , is an embedding and . Evidently, if F either determines or generates αX, then every elements of F has an extension to αX; whenever F satisfies this latter condition, the set of all such extensions is denoted Fα.A major results of our previous paper is that F determines αX if and only if Fα separates points of αX ? X. A major result of the present paper is that F generates αX if and only if Fα separates points of αX. 相似文献
20.
Harald Brandenburg 《Topology and its Applications》1983,15(3):223-229
A second countable developable T1-space 1 is defined which has the following properties: (1) 1 is an absolute extensor for the class of perfect spaces. (2) 1?0 is a universal space for second countable developable T1-spaces. 相似文献