共查询到20条相似文献,搜索用时 31 毫秒
1.
T.K. Subrahmonian Moothathu 《Topology and its Applications》2011,158(16):2232-2239
We look at the dynamics of continuous self-maps of compact metric spaces possessing the pseudo-orbit tracing property (i.e., the shadowing property). Among other things we prove the following: (i) the set of minimal points is dense in the non-wandering set Ω(f), (ii) if f has either a non-minimal recurrent point or a sensitive minimal subsystem, then f has positive topological entropy, (iii) if X is infinite and f is transitive, then f is either an odometer or a syndetically sensitive non-minimal map with positive topological entropy, (iv) if f has zero topological entropy, then Ω(f) is totally disconnected and f restricted to Ω(f) is an equicontinuous homeomorphism. 相似文献
2.
If X is a compact-covering image of a closed subspace of product of a σ-compact Polish space and a compact space, then Ck(X,M), the space of continuous maps of X into M with the compact-open topology, is stratifiable for any metric space M.If X is σ-compact Polish, K is compact and M metric then every point of Ck(X×K,M) has a closure-preserving local base, and hence this function space is M1. 相似文献
3.
We study the completeness of three (metrizable) uniformities on the sets D(X, Y) and U(X, Y) of densely continuous forms and USCO maps from X to Y: the uniformity of uniform convergence on bounded sets, the Hausdorff metric uniformity and the uniformity U B . We also prove that if X is a nondiscrete space, then the Hausdorff metric on real-valued densely continuous forms D(X, ?) (identified with their graphs) is not complete. The key to guarantee completeness of closed subsets of D(X, Y) equipped with the Hausdorff metric is dense equicontinuity introduced by Hammer and McCoy in [7]. 相似文献
4.
Risong Li 《Communications in Nonlinear Science & Numerical Simulation》2012,17(7):2815-2823
Let f : X → X be a continuous map of a compact metric space X. The map f induces in a natural way a map fM on the space M(X) of probability measures on X, and a transformation fK on the space K(X) of closed subsets of X. In this paper, we show that if (X, f) is a chain transitive system with shadowing property, then exactly one of the following two statements holds:
- (a)
- fn and (fK)n are syndetically sensitive for all n ? 1.
- (b)
- fn and (fK)n are equicontinuous for all n ? 1.
5.
Let M be the Cantor space or an n-manifold with C(M,M) the set of continuous self-maps of M. We prove the following:
- (1)
- There is a residual set of points (x,f) in M×C(M,M) all of which generate as their ω-limit set a particular, unique adding machine.
- (2)
- Moreover, if M has the fixed point property, then a generic f∈C(M,M) generates uncountably many distinct copies of every possible adding machine.
6.
Vegard Lima 《Journal of Mathematical Analysis and Applications》2007,334(1):593-603
We study the weak metric approximation property introduced by Lima and Oja. We show that a Banach space X has the weak metric approximation property if and only if F(Y,X), the space of finite rank operators, is an ideal in W(Y,X∗∗), the space of weakly compact operators for all Banach spaces Y. 相似文献
7.
Francisco BalibreaMarek Lampart Piotr Oprocha 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(6):3262-3267
In this paper we study the structure of negative limit sets of maps on the unit interval. We prove that every α-limit set is an ω-limit set, while the converse is not true in general. Surprisingly, it may happen that the space of all α-limit sets of interval maps is not closed in the Hausdorff metric (and thus some ω-limit sets are never obtained as α-limit sets). Moreover, we prove that the set of all recurrent points is closed if and only if the space of all α-limit sets is closed. 相似文献
8.
Surjit Singh Khurana 《Journal of Mathematical Analysis and Applications》1978,65(2):361-364
The following theorem is proved. If a locally convex space, quasi-complete for Mackey topology, has D-P (Dunford-Pettis) property then it has strict D-P property. Conversely, if (E′, σ(E′, E)) has a σ-compact dense subset and E has strict D-P property, then it has D-P property. Also it is proved that (Cb(X),) where F=β0, β, orβ1, has strict D-P property and (Cb(X), β0) has D-P property; if X contains a σ-compact dense subset then (Cb(X), β) and (Cb(X), β1) have D-P property. 相似文献
9.
Ju Myung Kim 《Journal of Mathematical Analysis and Applications》2008,345(2):889-891
This paper is concerned with the approximation property which is an important property in Banach space theory. We show that a Banach space X has the approximation property if (and only if), for every Banach space Y, the set of finite rank operators from X to Y is dense in the corresponding space of compact operators, in the usual topology of uniform convergence on compact sets. 相似文献
10.
It is well known that for dynamical systems generated by continuous maps of a graph, the centre of the dynamical system is a subset of the set of ω-limit points.In this paper we provide an example of a continuous self-map f1 of a dendrite such that ω(f1) is a proper subset of C(f1).The second example is a continuous self-map f2 of a dendrite having a strictly increasing sequence of ω-limit sets which is not contained in any maximal one. Again, this is impossible for continuous maps on graphs. 相似文献
11.
Zdeněk Ko?an Veronika Kurková Michal Málek 《Communications in Nonlinear Science & Numerical Simulation》2012,17(8):3169-3176
For interval maps and also for graph maps, every ω-limit set is a subset of a maximal one. In this note we construct a continuous map on a dendrite with no maximal ω-limit set. Moreover, the set of branch points is nowhere dense, every ω-limit set of the map is nowhere dense, the set of periodic points and the set of recurrent points are equal and the set of ω-limit points is not closed (an example with the last property was constructed by the authors already in [Ko?an Z, Kornecká-Kurková V, Málek M. On the centre and the set of omega-limit points of continuous maps on dendrites. Topol Appl 2009;156:2923-2931]). 相似文献
12.
For a Tychonoff space X, we use ↓USC(X) and ↓C(X) to denote the families of the regions below all upper semi-continuous maps and of the regions below all continuous maps from X to I=[0,1], respectively. In this paper, we consider the spaces ↓USC(X) and ↓C(X) topologized as subspaces of the hyperspace Cld(X×I) consisting of all non-empty closed sets in X×I endowed with the Vietoris topology. We shall prove that ↓USC(X) is homeomorphic (≈) to the Hilbert cube Q=ω[−1,1] if and only if X is an infinite compact metric space. And we shall prove that (↓USC(X),↓C(X))≈(Q,c0), where , if and only if ↓C(X)≈c0 if and only if X is a compact metric space and the set of isolated points is not dense in X. 相似文献
13.
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
14.
Let X be a topological space and let C(X) be the ring of all real-valued continuous functions defined on X. We study the representation and approximation of continuous functions by sums of infinite series. Among other results, we give sufficient conditions in order to represent or approximate every continuous function by infinite series of functions, belonging to a previously fixed subfamily of C(X), when X is either a locally compact paracompact space or a Lindelöf space. 相似文献
15.
M. Sakai 《Acta Mathematica Hungarica》2010,128(1-2):96-105
For a Tychonoff space X, we denote by C p (X) the space of real-valued continuous functions with the topology of pointwise convergence. We show that (a) Arhangel℉skii℉s property (α 2) and the Ramsey property introduced by Nogura and Shakhmatov are equivalent for C p (X), (b) the Ramsey property and Nyikos’ property (α 3/2) are not equivalent for C p (X). These results answer questions posed by Shakhmatov. Concerning properties (α i ) for C p (X), some results on Scheepers’ conjecture are also given. 相似文献
16.
Let A be a lattice-ordered algebra endowed with a topology compatible with the structure of algebra. We provide internal conditions for A to be isomorphic as lattice-ordered algebras and homeomorphic to Ck(X), the lattice-ordered algebra C(X) of real continuous functions on a completely regular and Hausdorff topological space X, endowed with the topology of uniform convergence on compact sets. As a previous step, we determine this topology among the locally m-convex topologies on C(X) with the property that each order closed interval is bounded. 相似文献
17.
We study the position of compact operators in the space of all continuous linear operators and its subspaces in terms of ideals. One of our main results states that for Banach spaces X and Y the subspace of all compact operators K (X, Y) is an M(r 1 r 2, s 1 s 2)-ideal in the space of all continuous linear operators L(X, Y) whenever K (X,X) and K (Y, Y) are M(r 1, s 1)- and M(r 2, s 2)-ideals in L(X,X) and L(Y, Y), respectively, with r 1 + s 1/2 > 1 and r 2 +s 2/2 > 1. We also prove that the M(r, s)-ideal K (X, Y ) in L(X, Y ) is separably determined. Among others, our results complete and improve some well-known results on M-ideals. 相似文献
18.
In this paper, the notion of the bounded compact approximation property (BCAP) of a pair [Banach space and its subspace] is used to prove that if X is a closed subspace of L∞ with the BCAP, then L∞/X has the BCAP. We also show that X* has the λ-BCAP with conjugate operators if and only if the pair (X, Y) has the λ-BCAP for each finite codimensional subspace Y∈X. Let M be a closed subspace of X such that M⊥ is complemented in X*. If X has the (bounded) approximation property of order p, then M has the (bounded) approximation property of order p. 相似文献
19.
Ju Myung Kim 《Journal of Mathematical Analysis and Applications》2006,324(1):721-727
It is shown that for the separable dual X∗ of a Banach space X, if X∗ has the weak approximation property, then X∗ has the metric weak approximation property. We introduce the properties W∗D and MW∗D for Banach spaces. Suppose that M is a closed subspace of a Banach space X such that M⊥ is complemented in the dual space X∗, where for all m∈M}. Then it is shown that if a Banach space X has the weak approximation property and W∗D (respectively, metric weak approximation property and MW∗D), then M has the weak approximation property (respectively, bounded weak approximation property). 相似文献
20.
Let X be a locally compact Polish space and G a non-discrete Polish ANR group. By C(X,G), we denote the topological group of all continuous maps endowed with the Whitney (graph) topology and by Cc(X,G) the subgroup consisting of all maps with compact support. It is known that if X is compact and non-discrete then the space C(X,G) is an l2-manifold. In this article we show that if X is non-compact and not end-discrete then Cc(X,G) is an (R∞×l2)-manifold, and moreover the pair (C(X,G),Cc(X,G)) is locally homeomorphic to the pair of the box and the small box powers of l2. 相似文献