共查询到20条相似文献,搜索用时 15 毫秒
1.
We give a proof of localic Priestley duality. Our approach is based on lax proper maps of locales, which provide a vehicle for presenting the Priestley version of full Stone duality constructively and preserve spatial intuitions. 相似文献
2.
Akira Koyama 《Topology and its Applications》1984,17(3):247-255
This paper studies properties of refinable maps and contains applications to dimension theory. It is proved that refinable maps between compact Hausdorff spaces preserve covering dimension exactly and do not raise small cohomological dimension with any coefficient group. The notion of a c-refinable map is introduced and is shown to play a comparable role in the setting of normal spaces. For example, c-refinable maps between normal spaces are shown to preserve covering dimension and S-weak infinite-dimensionality. These facts do not hold for refinable maps. 相似文献
3.
Alexander P. Pyshchev 《Topology and its Applications》2006,153(14):2730-2734
The following characterization of fully closed maps is proved: a quotient map between regular spaces is fully closed if and only if it coincides with the fiber product of elementary maps between regular spaces. 相似文献
4.
Within the class of Tychonoff spaces, and within the class of topological groups, most of the natural questions concerning ‘productive closure’ of the subclasses of countably compact and pseudocompact spaces are answered by the following three well-known results: (1) [ZFC] There is a countably compact Tychonoff space X such that X × X is not pseudocompact; (2) [ZFC] The product of any set of pseudocompact topological groups is pseudocompact; and (3) [ZFC+ MA] There are countably compact topological groups G0, G1 such that G0 × G1 is not countably compact.In this paper we consider the question of ‘productive closure” in the intermediate class of homogeneous spaces. Our principal result, whose proof leans heavily on a simple, elegant result of V.V. Uspenski?, is this: In ZFC there are pseudocompact, homogeneous spaces X0, X1 such that X0 × X1 is not pseudocompact; if in addition MA is assumed, the spaces Xi may be chosen countably compact.Our construction yields an unexpected corollary in a different direction: Every compact space embeds as a retract in a countably compact, homogeneous space. Thus for every cardinal number α there is a countably compact, homogeneous space whose Souslin number exceeds α. 相似文献
5.
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
6.
J. J. Charatonik 《Periodica Mathematica Hungarica》1985,16(4):219-236
It is proved that Knaster's type continua and solenoids can be considered as inverse limits of arcs and of circles with confluent bonding mappings. Several other classes of bonding mappings, which are relative to confluent ones, also are discussed. 相似文献
7.
Alexander Blokh Lex Oversteegen E.D. Tymchatyn 《Topology and its Applications》2006,153(10):1571-1585
A continuous map of topological spaces X,Y is said to be almost 1-to-1 if the set of the points x∈X such that f−1(f(x))={x} is dense in X; it is said to be light if pointwise preimages are 0-dimensional. In a previous paper we showed that sometimes almost one-to-one light maps of compact and σ-compact spaces must be homeomorphisms or embeddings. In this paper we introduce a similar notion of an almost d-to-1 map and extend the above results to them and other related maps. In a forthcoming paper we use these results and show that if f is a minimal self-mapping of a 2-manifold then point preimages under f are tree-like continua and either M is a union of 2-tori, or M is a union of Klein bottles permuted by f. 相似文献
8.
Klaas Pieter Hart 《Topology and its Applications》1983,15(2):151-158
We investigate separation properties of ω1-trees. We show that the property γ of Devlin and Shelah is equivalent to hereditary collectionwise normality. We show that monotone normality and divisibility are both equivalent to orderability. Finally we show that Souslin trees are examples of trees with property γ which are not retractable. 相似文献
9.
The simplest condition characterizing quasi-finite CW complexes K is the implication XτhK⇒β(X)τK for all paracompact spaces X. Here are the main results of the paper:
Theorem 0.1.
If{Ks}s∈Sis a family of pointed quasi-finite complexes, then their wedge?s∈SKsis quasi-finite. 相似文献
10.
Jonathan David Farley 《Order》1996,13(1):65-98
The category of bounded distributive lattices with order-preserving maps is shown to be dually equivalent to the category of Priestley spaces with Priestley multirelations. The Priestley dual space of the ideal lattice L
of a bounded distributive lattice L is described in terms of the dual space of L. A variant of the Nachbin-Stone-ech compactification is developed for bitopological and ordered spaces. Let X be a poset and Y an ordered space; X
Y
denotes the poset of continuous order-preserving maps from Y to X with the discrete topology. The Priestley dual of L
P
is determined, where P is a poset and L a bounded distributive lattice. 相似文献
11.
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
12.
B.A. Pasynkov 《Topology and its Applications》2010,157(4):730-744
Let Iτ be the Tychonoff cube of weight τ?ω with a fixed point, στ and Στ be the correspondent σ- and Σ-products in Iτ and στ⊂(Σστ=ω(στ))⊂Στ. Then for any n∈{0,1,2,…}, there exists a compactum Unτ⊂Iτ of dimension n such that for any Z⊂Iτ of dimension?n, there exists a topological embedding of Z in Unτ that maps the intersections of Z with στ, Σστ and Στ to the intersections , and of Unτ with στ, Σστ and Στ, respectively; , and are n-dimensional and is σ-compact, is a Lindelöf Σ-space and is a sequentially compact normal Fréchet-Urysohn space. This theorem (on multistage universal spaces of given dimension and weight) implies multistage extension theorems (in particular, theorems on Corson and Eberlein compactifications) for Tychonoff spaces. 相似文献
13.
14.
We establish the existence of universal G-spaces for proper actions of locally compact groups on Tychonoff spaces. A typical result sounds as follows: for each infinite cardinal number τ every locally compact, non-compact, σ-compact group G of weight w(G)?τ, can act properly on Rτ?{0} such that Rτ?{0} contains a G-homeomorphic copy of every Tychonoff proper G-space of weight ?τ. The metric cones Cone(G/H) with H⊂G a compact subgroup such that G/H is a manifold, are the main building blocks in our approach. As a byproduct we prove that the cardinality of the set of all conjugacy classes of such subgroups H⊂G does not exceed the weight of G. 相似文献
15.
We consider different types of topologies on the set of functions between two ?ech closure spaces and investigate some of their properties. 相似文献
16.
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
17.
L.Gaunce Lewis 《Topology and its Applications》1985,19(1):75-89
We show that pulling back along an open map preserves all colimits in the category of weak Hausdorff k-spaces. We also show that the category of open maps over a weak Hausdorff k-space is a convenient category of fibre spaces. 相似文献
18.
S. Miklos 《Topology and its Applications》1985,20(2):143-147
We characterize dendrites which admit an open retraction onto an arbitrary n-od. The paper contains also several corollaries and two problems concerning the subject 相似文献
19.
Piotr Minc 《Topology and its Applications》2006,153(11):1895-1916
In this paper, we answer a question by Krasinkiewicz, Reńska and Sobolewski by constructing countable connected Hausdorff and Urysohn spaces as quotient spaces of bunches of arcs in the plane. We also consider a generalization of graphs by allowing vertices to be continua and replacing edges by not necessarily connected sets. We require only that two “vertices” be in the same quasi-component of the “edge” that contains them. We observe that if a graph G cannot be embedded in the plane, then any generalized graph modeled on G is not embeddable in the plane. As a corollary we obtain not planar bunches of arcs with their natural quotients Hausdorff or Urysohn. This answers another question by Krasinkiewicz, Reńska and Sobolewski. 相似文献
20.
Günther Richter 《Topology and its Applications》1985,20(1):79-87
Full subcategories C ? Top of the category of topological spaces, which are algebraic over Set in the sense of Herrlich [2], have pleasant separation properties, mostly subject to additional closedness assumptions. For instance, every C-object is a T1-space, if the two-element discrete space belongs to C. Moreover, if C is closed under the formation of finite powers in Top and even varietal [2], then every C-object is Hausdorff. Hence, the T2-axiom turns out to be (nearly) superfluous in Herrlich's and Strecker's characterization of the category of compact Hausdorff spaces [1], although it is essential for the proof.If we think of C-objects X as universal algebras (with possibly infinite operations), then the subalgebras of X form the closed sets of a compact topology on X, provided that the ordinal spaces [0, β] belong to C. This generalizes a result in [3]. The subalgebra topology is used to prove criterions for the Hausdorffness of every space in C, if C is only algebraic. 相似文献