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1.
Recently the authors have defined a coherent prohomotopy category of topological spaces CPHTop [5]. In the present paper, which is a sequel to Part I [6], the authors define a strong homology functor Hs:CPHTop→Ab. The results of this paper are essential for the construction of a Steenrod-Sitnikov homology theory for arbitrary spaces. 相似文献
2.
Sibe Marde
i 《Topology and its Applications》1988,30(3):291-306
The well-known factorization theorems for covering dimension dim and compact Hausdorff spaces are here established for the cohomological dimension dim
using a new characterization of dim
In particular, it is proved that every mapping f: X → Y from a compact Hausdorff space X with
to a compact metric space Y admits a factorization f = hg, where g: X → Z, h: Z → Y and Z is a metric compactum with
. These results are applied to the well-known open problem whether
. It is shown that the problem has a positive answer for compact Hausdorff spaces X if and only if it has a positive answer for metric compacta X. 相似文献
3.
Álvarez A. Bravo J. L. Christopher C. Mardešić P. 《Functional Analysis and Its Applications》2021,55(4):257-271
Functional Analysis and Its Applications - We study the analog of the classical infinitesimal center problem in the plane, but for zero cycles. We define the displacement function in this context... 相似文献
4.
Functoriality of the standard resolution of the Cartesian product of a compactum and a polyhedron II
Sibe Mardeši? 《Topology and its Applications》2008,155(15):1708-1719
In 2003 the author has associated with every cofinite inverse system of compact Hausdorff spaces X with limit X and every simplicial complex K (possibly infinite) with geometric realization P=|K| a resolution R(X,K) of X×P, which consists of paracompact spaces. If X consists of compact polyhedra, then R(X,K) consists of spaces having the homotopy type of polyhedra. In a subsequent paper, published in 2007, the author proved that R(X,K) is a covariant functor in the first variable. In the present paper it is proved that R(X,K) is a covariant functor also in the second variable. 相似文献
5.
We consider families of Abelian integrals arising from perturbations of planar Hamiltonian systems. The tangential center-focus problem asks for conditions under which these integrals vanish identically. The problem is closely related to the monodromy problem, which asks when the monodromy of a vanishing cycle generates the whole homology of the level curves of the Hamiltonian.
We solve both of these questions for the case in which the Hamiltonian is hyperelliptic. As a by-product, we solve the corresponding
problems for the 0-dimensional Abelian integrals defined by Gavrilov and Movasati. 相似文献
6.
Pavao Mardešić Dmitry Novikov Laura Ortiz-Bobadilla Jessie Pontigo-Herrera 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(7):1941-1957
In this paper we study polynomial Hamiltonian systems in the plane and their small perturbations: . The first nonzero Melnikov function of the Poincaré map along a loop γ of is given by an iterated integral [3]. In [7], we bounded the length of the iterated integral by a geometric number which we call orbit depth. We conjectured that the bound is optimal.Here, we give a simple example of a Hamiltonian system F and its orbit γ having infinite orbit depth. If our conjecture is true, for this example there should exist deformations with arbitrary high length first nonzero Melnikov function along γ. We construct deformations whose first nonzero Melnikov function is of length three and explain the difficulties in constructing deformations having high length first nonzero Melnikov functions . 相似文献
7.
In previous parts I and II of this paper [4] strong homology groups of inverse systems were introduced and studied. In this part III of the paper we define strong homology groups of inverse systems of pairs and show that they have suitable exactness and excision properties. As a consequence of these results the Steenrod-Sitnikov homology [1] for pairs (X,A), where X is a paracompact space and A is a closed subset of X, is exact and satisfies the excision axiom. 相似文献
8.
In the literature there exist examples of separable metric spaces
X,Y whose Cartesian product X × Y is not a product in the shape category
Sh(Top). It is an open question whether, for X a compact Hausdorff space,
X × Y is a product in Sh(Top), for every topological spaces Y. The main
result of the paper asserts that the answer is positive provided X × P is a
product in Sh(Top), for every polyhedron P. 相似文献
9.
Sibe Mardeši? 《Topology and its Applications》2007,155(1):1-32
In a previous paper the author has associated with every inverse system of compact Hausdorff spaces X with limit X and every simplicial complex K (possibly infinite) with geometric realization P=|K| a resolution RK(X) of X×P, which consists of paracompact spaces. If X consists of compact polyhedra, then RK(X) consists of spaces having the homotopy type of polyhedra. In the present paper it is proved that this construction is functorial. One of the consequences is the existence of a functor from the strong shape category of compact Hausdorff spaces X to the shape category of spaces, which maps X to the Cartesian product X×P. Another consequence is the theorem which asserts that, for compact Hausdorff spaces X, X′, such that X is strong shape dominated by X′ and the Cartesian product X′×P is a direct product in Sh(Top), then also X×P is a direct product in the shape category Sh(Top). 相似文献
10.
We study the relationship between the multiplicity of a fixed point of a function g, and the dependence on ε of the length of ε-neighborhood of any orbit of g, tending to the fixed point. The relationship between these two notions was discovered in Elezovi?, ?ubrini? and ?upanovi? (2007) [5] in the differentiable case, and related to the box dimension of the orbit.Here, we generalize these results to non-differentiable cases introducing a new notion of critical Minkowski order. We study the space of functions having a development in a Chebyshev scale and use multiplicity with respect to this space of functions. With the new definition, we recover the relationship between multiplicity of fixed points and the dependence on ε of the length of ε-neighborhoods of orbits in non-differentiable cases.Applications include in particular Poincaré maps near homoclinic loops and hyperbolic 2-cycles, and Abelian integrals. This is a new approach to estimate the cyclicity, by computing the length of the ε-neighborhood of one orbit of the Poincaré map (for example numerically), and by comparing it to the appropriate scale. 相似文献