共查询到20条相似文献,搜索用时 296 毫秒
1.
2.
Any continuous map T on a compact metric space X induces in a natural way a continuous map on the space K(X) of all non-empty compact subsets of X. Let T be a homeomorphism on the interval or on the circle. It is proved that the topological entropy of the induced set valued map is zero or infinity. Moreover, the topological entropy of is zero, where C(X) denotes the space of all non-empty compact and connected subsets of X. For general continuous maps on compact metric spaces these results are not valid. 相似文献
3.
Helge Glöckner 《Journal of Functional Analysis》2007,245(1):19-61
Let G be a Lie group which is the union of an ascending sequence G1⊆G2⊆? of Lie groups (all of which may be infinite-dimensional). We study the question when in the category of Lie groups, topological groups, smooth manifolds, respectively, topological spaces. Full answers are obtained for G the group Diffc(M) of compactly supported C∞-diffeomorphisms of a σ-compact smooth manifold M; and for test function groups of compactly supported smooth maps with values in a finite-dimensional Lie group H. We also discuss the cases where G is a direct limit of unit groups of Banach algebras, a Lie group of germs of Lie group-valued analytic maps, or a weak direct product of Lie groups. 相似文献
4.
Pavle V.M. Blagojevi? Aleksandra S. Dimitrijevi? Blagojevi? John McCleary 《Topology and its Applications》2008,156(1):16-23
Let be a Jordan curve in the plane. It is a simple topological riddle to determine if there is an equilateral triangle with vertices on γ. By reformulating this question in the paradigm of configuration spaces and test maps, we can solve this riddle using a Borsuk-Ulam type theorem obtained using equivariant methods. 相似文献
5.
Let (X,T) be a topological dynamical system and be a sub-additive potential on C(X,R). Let U be an open cover of X. Then for any T-invariant measure μ, let . The topological pressure for open covers U is defined for sub-additive potentials. Then we have a variational principle:
6.
Let T be a positive closed (p,p)-current on a compact Kähler manifold X. We prove the existence of smooth positive closed (p,p)-forms and such that weakly. Moreover, where cX>0 is a constant independent of T. We also extend this result to positive pluriharmonic currents. Then we study the wedge product of positive closed (1,1)-currents having continuous potential with positive pluriharmonic currents. As an application, we give an estimate for the topological entropy of meromorphic maps on compact Kähler manifolds. 相似文献
7.
Dali Zangurashvili 《Journal of Pure and Applied Algebra》2007,209(1):255-267
The paper deals with the question whether it is sufficient, when investigating the problem of the effectiveness of a descent morphism, to restrict the consideration only to the descent data (C,γ,ξ), where γ lies in a certain morphism class. The notion of a factorization system and the dual to the amalgamation property in the sense of Kiss, Marki, Pröhle and Tholen play the key role in our discussion.It is shown that a category inherits from a category the property that all descent morphisms are effective if either is regular and is a full coreflective, closed under pullbacks of certain epimorphisms, subcategory of or is regular, has coequalizers and there exists a topological functor . This implies that in the category of topological spaces, all regular monomorphisms are effective codescent morphisms (the result of Mantovani). The same is shown to be valid also for the categories of compact Hausdorff topological spaces, normal topological spaces, Banach spaces, (quasi-)uniform spaces, and (quasi-)proximity spaces. Moreover, the effectiveness of all codescent morphisms is established for the categories of Hausdorff topological spaces and (complete) metric spaces. The internal characterization of such morphisms p:B→E is given for the category of Hausdorff topological spaces, in the case of compact B and regular E. 相似文献
8.
9.
Hiroaki Terao 《Advances in Mathematics》2007,214(1):366-378
Let A be a nonempty real central arrangement of hyperplanes and Ch be the set of chambers of A. Each hyperplane H defines a half-space H+ and the other half-space H−. Let B={+,−}. For H∈A, define a map by (if C⊆H+) and (if C⊆H−). Define . Let Chm=Ch×Ch×?×Ch (m times). Then the maps induce the maps . We will study the admissible maps which are compatible with every . Suppose |A|?3 and m?2. Then we will show that A is indecomposable if and only if every admissible map is a projection to a component. When A is a braid arrangement, which is indecomposable, this result is equivalent to Arrow's impossibility theorem in economics. We also determine the set of admissible maps explicitly for every nonempty real central arrangement. 相似文献
10.
Marcelo A. Aguilar 《Topology and its Applications》2007,154(15):2826-2848
Let M be a Mackey functor for a finite group G. In this paper, generalizing the Dold-Thom construction, we construct an ordinary equivariant homotopical homology theory with coefficients in M, whose values on the category of finite G-sets realize the bifunctor M, both covariantly and contravariantly. Furthermore, we extend the contravariant functor to define a transfer in the theory for G-equivariant covering maps. This transfer is given by a continuous homomorphism between topological abelian groups.We prove a formula for the composite of the transfer and the projection of a G-equivariant covering map and characterize those Mackey functors M for which that formula has an expression analogous to the classical one. 相似文献
11.
韩友发 《数学物理学报(B辑英文版)》2011,31(3):1011-1019
The central subject of studying in this paper is incompressible pairwise incompressible surfaces in link complements. Let L be a non-split prime link and let F be an incompressible pairwise incompressible surface in S~3 - L. We discuss the properties that the surface F intersects with 2-spheres in S~3 - L. The intersection forms a topological graph consisting of a collection of circles and saddle-shaped discs. We introduce topological graphs and their moves (R-move and S~2-move), and define the characteristic number of the topological graph for F∩S~2±. The characteristic number is unchanged under the moves. In fact, the number is exactly the Euler Characteristic number of the surface when a graph satisfies some conditions. By these ways, we characterize the properties of incompressible pairwise incompressible surfaces in alternating (or almost alternating) link complements. We prove that the genus of the surface equals zero if the component number of F∩S~2+(or F∩S~2-) is less than five and the graph is simple for alternating or almost alternating links. Furthermore, one can prove that the genus of the surface is zero if #(F) ≤8. 相似文献
12.
13.
14.
Biagio Ricceri 《Topology and its Applications》2006,153(17):3308-3312
In this paper, we establish some minimax theorems, of purely topological nature, that, through the variational methods, can be usefully applied to nonlinear differential equations. Here is a (simplified) sample: Let X be a Hausdorff topological space, I⊆R an interval and . Assume that the function Ψ(x,⋅) is lower semicontinuous and quasi-concave in I for all x∈X, while the function Ψ(⋅,q) has compact sublevel sets and one local minimum at most for each q in a dense subset of I. Then, one has
15.
Ji?í Spurný 《Journal of Functional Analysis》2006,232(2):259-294
Let X be a compact convex subset of a locally convex space. We show that any bounded Baire-one function defined on can be extended to an affine Baire-one function on X if and only if X is a Choquet simplex and satisfies a certain topological property. 相似文献
16.
Given a metric Peano continuum X we introduce and study the Hölder Dimension there is a -Hölder onto map of X as well as its topological counterpart is an admissible metric for X}. We show that for each convex metric continuum X the dimension Hö-dim(X) equals the fractal dimension of X. The topological Hölder dimension Hö-dim(Mn) of the n-dimensional universal Menger cube Mn equals n. On the other hand, there are 1-dimensional rim-finite Peano continua X with arbitrary prescribed Hö-dim(X)?1. 相似文献
17.
Alexander Brudnyi 《Bulletin des Sciences Mathématiques》2008,132(3):165
We study some algebraic and topological objects that appear naturally in the study of the center problem for the ordinary differential equation . In particular, we give a topological characterization of Lipschitz curves defined by the first integrals of the coefficients of this equation such that all moments of order?n, n∈N, vanish on them. 相似文献
18.
Karim Samei 《Journal of Pure and Applied Algebra》2007,209(3):813-821
In this paper the zero-divisor graph Γ(R) of a commutative reduced ring R is studied. We associate the ring properties of R, the graph properties of Γ(R) and the topological properties of . Cycles in Γ(R) are investigated and an algebraic and a topological characterization is given for the graph Γ(R) to be triangulated or hypertriangulated. We show that the clique number of Γ(R), the cellularity of and the Goldie dimension of R coincide. We prove that when R has the annihilator condition and ; Γ(R) is complemented if and only if is compact. In a semiprimitive Gelfand ring, it turns out that the dominating number of Γ(R) is between the density and the weight of . We show that Γ(R) is not triangulated and the set of centers of Γ(R) is a dominating set if and only if the set of isolated points of is dense in . 相似文献
19.
If the Aubry set satisfies some topological hypothesis, such as H1(M×T,A(c),R)≠0, then the α-function has a flat. In this paper, we will prove that has infinitely many -minimal homoclinic orbits when c′ is on the boundary of the maximal flat of the α-function. These homoclinic orbits are different from the usually called multi-bump solutions. 相似文献
20.
It was discovered some years ago that there exist non-integer real numbers q>1 for which only one sequence (ci) of integers ci∈[0,q) satisfies the equality . The set of such “univoque numbers” has a rich topological structure, and its study revealed a number of unexpected connections with measure theory, fractals, ergodic theory and Diophantine approximation.In this paper we consider for each fixed q>1 the set Uq of real numbers x having a unique representation of the form with integers ci belonging to [0,q). We carry out a detailed topological study of these sets. For instance, we characterize their closures, and we determine those bases q for which Uq is closed or even a Cantor set. We also study the set consisting of all sequences (ci) of integers ci∈[0,q) such that . We determine the numbers r>1 for which the map (defined on (1,∞)) is constant in a neighborhood of r and the numbers q>1 for which is a subshift or a subshift of finite type. 相似文献