共查询到20条相似文献,搜索用时 15 毫秒
1.
Naotsugu Chinen 《Topology and its Applications》2012,159(4):1236-1245
In this paper, we decide the exact value of the color number of a fixed point free homeomorphism on a connected locally finite graph. We prove that for every fixed-point free homeomorphism from a connected locally finite graph into itself, the greatest common divisor of all period for its map is equal to one or three if and only if its color number is 4. 相似文献
2.
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
3.
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
4.
The space PK of partial maps with compact domains (identified with their graphs) forms a subspace of the hyperspace of nonempty compact subsets of a product space endowed with the Vietoris topology. Various completeness properties of PK, including ?ech-completeness, sieve completeness, strong Choquetness, and (hereditary) Baireness, are investigated. Some new results on the hyperspace K(X) of compact subsets of a Hausdorff X with the Vietoris topology are obtained; in particular, it is shown that there is a strongly Choquet X, with 1st category K(X). 相似文献
5.
Hisao Kato 《Topology and its Applications》2007,154(6):1027-1031
In [G.T. Seidler, The topological entropy of homeomorphisms on one-dimensional continua, Proc. Amer. Math. Soc. 108 (1990) 1025-1030], G.T. Seidler proved that the topological entropy of every homeomorphism on a regular curve is zero. Also, in [H. Kato, Topological entropy of monotone maps and confluent maps on regular curves, Topology Proc. 28 (2) (2004) 587-593] the topological entropy of confluent maps on regular curves was investigated. In particular, it was proved that the topological entropy of every monotone map on any regular curve is zero. In this paper, furthermore we investigate the topological entropy of more general maps on regular curves. We evaluate the topological entropy of maps f on regular curves X in terms of the growth of the number of components of f−n(y) (y∈X). 相似文献
6.
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
7.
8.
Given a metric continuum X, we consider the following hyperspaces of X : 2X, Cn(X) and Fn(X) (n∈N). Let F1(X)={{x}:x∈X}. A hyperspace K(X) of X is said to be rigid provided that for every homeomorphism h:K(X)→K(X) we have that h(F1(X))=F1(X). In this paper we study under which conditions a continuum X has a rigid hyperspace Fn(X). 相似文献
9.
Galo Higuera Alejandro Illanes 《Topology and its Applications》2012,159(1):1-6
For a metric continuum X, let Fn(X)={A⊂X:A is nonempty and has at most n points}. In this paper we show a continuum X such that F2(X) has the fixed point property while X does not have it. 相似文献
10.
Generalizing results by J. Ford, J. W. Rogers, Jr. and H. Kato we prove that (1) a map f from a G-like continuum onto a graph G is refinable iff f is monotone; (2) a graph G is an arc or a simple closed curve iff every G-like continuum that contains no nonboundary indecomposable subcontinuum admits a monotone map onto G.We prove that if bonding maps in the inverse sequence of compact spaces are refinable then the projections of the inverse limit onto factor spaces are refinable. We use this fact to show that refinable maps do not preserve completely regular or totally regular continua. 相似文献
11.
For a metric continuum X, we consider the hyperspaces X2 and C(X) of the closed and nonempty subsets of X and of subcontinua of X, respectively, both with the Hausdorff metric. For a given map we investigate the transitivity of the induced maps and . Among other results, we show that if X is a dendrite or a continuum of type λ and is a map, then C(f) is not transitive. However, if X is the Hilbert cube, then there exists a transitive map such that f2 and C(f) are transitive. 相似文献
12.
L.F. Midolo 《Topology and its Applications》2009,156(7):1186-1191
We study, via continuous selections of multivalued maps, the problem of finding a right inverse to the restriction of a linear map to a convex body. 相似文献
13.
We prove that if for a continuous map f on a compact metric space X, the chain recurrent set, R(f) has more than one chain component, then f does not satisfy the asymptotic average shadowing property. We also show that if a continuous map f on a compact metric space X has the asymptotic average shadowing property and if A is an attractor for f, then A is the single attractor for f and we have A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if M is a compact manifold which is not finite with dimM=2, then the C1 interior of the set of all C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of Ω-stable diffeomorphisms. 相似文献
14.
Alicia Santiago-Santos 《Topology and its Applications》2011,158(16):2125-2139
15.
Alejandro Illanes 《Topology and its Applications》2011,158(5):653-659
Given a metric continuum X, let X2 and C(X) denote the hyperspaces of all nonempty closed subsets and subcontinua, respectively. For A,B∈X2 we say that B does not block A if A∩B=∅ and the union of all subcontinua of X intersecting A and contained in X−B is dense in X. In this paper we study some sets of blockers for several kinds of continua. In particular, we determine their Borel classes and, for a large class of locally connected continua X, we recognize them as cap-sets. 相似文献
16.
Dominik Kwietniak 《Topology and its Applications》2012,159(1):19-27
Let f be a continuous map of a compact metric space. Assuming shadowing for f we relate the average shadowing property of f to transitivity and its variants. Our results extend and complete the work of Sakai [K. Sakai, Various shadowing properties for positively expansive maps, Topology Appl. 131 (2003) 15-31]. 相似文献
17.
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
18.
Enrique Castañeda 《Topology and its Applications》2006,153(9):1434-1450
Let X be a metric continuum and let Fn(X) be the nth symmetric product of X (Fn(X) is the hyperspace of nonempty subsets of X with at most n points). In this paper we prove that if Fn(X) is homeomorphic to Fn(Y), where X is a finite graph and Y is a continuum, then X is homeomorphic to Y. 相似文献
19.
For a large class of metric spaces X including discrete groups we prove that the asymptotic Assouad-Nagata dimension AN-asdimX of X coincides with the covering dimension dim(νLX) of the Higson corona of X with respect to the sublinear coarse structure on X. Then we apply this fact to prove the equality AN-asdim(X×R)=AN-asdimX+1. We note that the similar equality for Gromov's asymptotic dimension asdim generally fails to hold [A. Dranishnikov, Cohomological approach to asymptotic dimension, Preprint, 2006].Additionally we construct an injective map from the asymptotic cone without the basepoint to the sublinear Higson corona. 相似文献
20.
We construct an example of a non-metric perfectly normal hereditarily indecomposable continuum. The example is constructed as an inverse limit of non-metric analogues of solenoids. Theorems needed to insure perfect normality are stated and proven. It is shown that the example cannot be embedded in a countable product of Hausdorff arcs. 相似文献