共查询到20条相似文献,搜索用时 62 毫秒
1.
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
2.
Takamitsu Yamauchi 《Topology and its Applications》2008,155(8):916-922
It is shown that if X is a countably paracompact collectionwise normal space, Y is a Banach space and φ:X→Y2 is a lower semicontinuous mapping such that φ(x) is Y or a compact convex subset with Cardφ(x)>1 for each x∈X, then φ admits a continuous selection f:X→Y such that f(x) is not an extreme point of φ(x) for each x∈X. This is an affirmative answer to the problem posed by V. Gutev, H. Ohta and K. Yamazaki [V. Gutev, H. Ohta and K. Yamazaki, Selections and sandwich-like properties via semi-continuous Banach-valued functions, J. Math. Soc. Japan 55 (2003) 499-521]. 相似文献
3.
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
4.
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
5.
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
6.
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
7.
A continuous function f from a continuum X onto a continuum Y is quasi-monotone if, for every subcontinuum M of Y with nonvoid interior, f-1(M) has a finite number of components each of which is mapped onto M by f. A θn-continuum is one that no subcontinuum separates into more than n components. It is known that if f is quasi-monotone and X is a θ1-continuum, then Y is a θ1-continuum or a θ2-continuum that is irreducible between two points. Examples are given to show that this cannot be generalized to a θn-continuum and n + 1 points for any n >1, but it is proved that if f is quasi-monotone and X is a θn-continuum, then Y is a θn-continuum or a θn+1-continuum that is the union of n + 2 continua H,S1,S2,…,Sn+1, whe for each i, Si is the closure of a component of Y H, Si is irreducible from some point Pi to H, and H is irreducible about its boundary. Some theorems and examples are given concerning the preservation of decomposition elements by a quasi-monotone map defined on a θn-continuum that admits a monotone, upper-semicontinuous decomposition onto a finite graph. 相似文献
8.
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
9.
M.R. Koushesh 《Topology and its Applications》2011,158(3):509-532
A space Y is called an extension of a space X if Y contains X as a dense subspace. Two extensions of X are said to be equivalent if there is a homeomorphism between them which fixes X point-wise. For two (equivalence classes of) extensions Y and Y′ of X let Y?Y′ if there is a continuous function of Y′ into Y which fixes X point-wise. An extension Y of X is called a one-point extension of X if Y?X is a singleton. Let P be a topological property. An extension Y of X is called a P-extension of X if it has P.One-point P-extensions comprise the subject matter of this article. Here P is subject to some mild requirements. We define an anti-order-isomorphism between the set of one-point Tychonoff extensions of a (Tychonoff) space X (partially ordered by ?) and the set of compact non-empty subsets of its outgrowth βX?X (partially ordered by ⊆). This enables us to study the order-structure of various sets of one-point extensions of the space X by relating them to the topologies of certain subspaces of its outgrowth. We conclude the article with the following conjecture. For a Tychonoff spaces X denote by U(X) the set of all zero-sets of βX which miss X.
Conjecture.
For locally compact spaces X and Y the partially ordered sets(U(X),⊆)and(U(Y),⊆)are order-isomorphic if and only if the spacesclβX(βX?υX)andclβY(βY?υY)are homeomorphic. 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.
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.
Alan Dow 《Topology and its Applications》1983,15(3):239-246
It is shown that ω × Yω does not have remote points if Y is a compact space with cellularity larger than ω1. It is also shown that it is consistent that ω × Yω does not have remote points if Y is compact with uncountable cellularity. As an application we construct a compact space with weight ω2 · c which can be covered by nowhere dense P-sets and a compact space with weight c for which it is independent that it can be covered by nowhere dense P-sets. 相似文献
13.
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
14.
Jie-Hua Mai 《Topology and its Applications》2011,158(16):2216-2220
Let X be a topological space, f:X→X be a continuous map, and Y be a compact, connected and closed subset of X. In this paper we show that, if the boundary X∂Y contains exactly one point v and f(v)∈Y, then Y contains a minimal set of f. 相似文献
15.
Oleg Okunev 《Topology and its Applications》2011,158(16):2158-2164
We prove that if X and Y are t-equivalent spaces (that is, if Cp(X) and Cp(Y) are homeomorphic), then there are spaces Zn, locally closed subspaces Bn of Zn, and locally closed subspaces Yn of Y, n∈N+, such that each Zn admits a perfect finite-to-one mapping onto a closed subspace of Xn, Yn is an image under a perfect mapping of Bn, and Y=?{Yn:n∈N+}. It is deduced that some classes of spaces, which for metric spaces coincide with absolute Borelian classes, are preserved by t-equivalence. Also some limitations on the complexity of spaces t-equivalent to “nice” spaces are obtained. 相似文献
16.
17.
E. Michael 《Topology and its Applications》2011,158(13):1526-1528
Principal result: Suppose Y is metrizable. Then: (a) if X is metrizable and A⊂X is closed, then every continuous g:A→Y extends to an l.s.c. ψ:X→K(Y); (b) Y satisfies (a) for all paracompact X if and only if Y is completely metrizable. 相似文献
18.
In Bani?, ?repnjak, Merhar and Milutinovi? (2010) [2] the authors proved that if a sequence of graphs of surjective upper semi-continuous set-valued functions fn:X→X2 converges to the graph of a continuous single-valued function f:X→X, then the sequence of corresponding inverse limits obtained from fn converges to the inverse limit obtained from f. In this paper a more general result is presented in which surjectivity of fn is not required. The result is also generalized to the case of inverse sequences with non-constant sequences of bonding maps. Finally, these new theorems are applied to inverse limits with tent maps. Among other applications, it is shown that the inverse limits appearing in the Ingram conjecture (with a point added) form an arc. 相似文献
19.
Alexey Ostrovsky 《Topology and its Applications》2009,156(9):1749-1751
The aim of this note is to prove the following result:Assume that f is a continuous function from the space of irrationals ωω onto Y such that the image f(U) of every set U which is open and closed in ωω is the union of one open and one closed set. Then Y is a completely metrizable space. 相似文献