共查询到20条相似文献,搜索用时 0 毫秒
1.
Paul Fabel 《Topology and its Applications》2007,154(3):635-638
With a certain natural topology, the fundamental group of a locally path connected metric space X becomes discrete if and only if X is semilocally simply connected. We include some related material and offer a counterexample to a similar result. 相似文献
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We prove that the notion of an inductive category in a model category agrees with the Ganea approach given by Doeraene. This notion also coincides with the topological one when we consider the category of (well-)pointed topological spaces. An application is given. 相似文献
4.
对广义近似空间之间的映射引入并刻画了粗糙连续性和拓扑连续性,探讨了他们的性质及相互关系.证明了两个粗糙连续映射的复合还是粗糙连续的,每个粗糙连续的映射都是拓扑连续的.在此基础上引入了粗糙同胚性质和拓扑同胚性质的概念,证明了拓扑同胚性质均为粗糙同胚性质并考察了广义近似空间的诸如分离性、连通性、紧性等的粗糙同胚不变性和拓扑同胚不变性. 相似文献
5.
L.Gaunce Lewis 《Topology and its Applications》1985,19(1):75-89
We show that pulling back along an open map preserves all colimits in the category of weak Hausdorff k-spaces. We also show that the category of open maps over a weak Hausdorff k-space is a convenient category of fibre spaces. 相似文献
6.
Alexandru E. Stanculescu 《Journal of Pure and Applied Algebra》2010,214(5):629-633
We prove that for certain monoidal (Quillen) model categories, the category of comonoids therein also admits a model structure. 相似文献
7.
《Expositiones Mathematicae》2019,37(1):2-24
We give a complete and careful proof of Quillen’s theorem on the existence of the standard model category structure on the category of topological spaces. We do not assume any familiarity with model categories. 相似文献
8.
Solomon Jekel 《Journal of Pure and Applied Algebra》2011,215(11):2628-2638
Let Gτ be the topological group of orientation preserving homeomorphisms of the circle, and Gδ the same group with the discrete topology. Motivated by the classical problem of reducing a circle bundle with structure group Gτ to a totally disconnected subgroup K⊂Gδ, and more currently, applications to mapping class groups, we analyze, in a homological algebra setting, the role played by the Topological and Discrete Euler Classes. In particular we describe the Discrete Euler Class of G, and any of its subgroups K, explicitly as a group extension. We apply our constructions to show that the values of the Discrete Euler Class are bounded on any space, and we state triviality and non-triviality conditions for its powers in the based mapping class groups. 相似文献
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Jean-Paul Doeraene Enrique Macias-Virgós Daniel Tanré 《Topology and its Applications》2010,157(9):1680-1689
This work solves the problem of elaborating Ganea and Whitehead definitions for the tangential category of a foliated manifold. We develop these two notions in the category S-Top of stratified spaces, that are topological spaces X endowed with a partition F and compare them to a third invariant defined by using open sets. More precisely, these definitions apply to an element (X,F) of S-Top together with a class A of subsets of X; they are similar to invariants introduced by M. Clapp and D. Puppe.If (X,F)∈S-Top, we define a transverse subset as a subspace A of X such that the intersection S∩A is at most countable for any S∈F. Then we define the Whitehead and Ganea LS-categories of the stratified space by taking the infimum along the transverse subsets. When we have a closed manifold, endowed with a C1-foliation, the three previous definitions, with A the class of transverse subsets, coincide with the tangential category and are homotopical invariants. 相似文献
11.
R.N. Karasev 《Topology and its Applications》2009,156(14):2406-2415
In this paper configuration spaces of smooth manifolds are considered. The accent is made on actions of certain groups (mostly p-tori) on this spaces by permuting their points. For such spaces the cohomological index, the genus in the sense of Krasnosel'skii-Schwarz, and the equivariant Lyusternik-Schnirelmann category are estimated from below, and some corollaries for functions on configuration spaces are deduced. 相似文献
12.
The Banach fixed point theorem in fuzzy quasi-metric spaces with application to the domain of words 总被引:1,自引:0,他引:1
We present a fuzzy quasi-metric version of the Banach contraction principle, which constitutes an extension of the famous Grabiec fixed point theorem. By using this result we show the existence of fixed point for contraction mappings on the domain of words when it is endowed with certain fuzzy quasi-metrics of Baire type. We apply this approach to deduce the existence of solution for some recurrence equations associated to the analysis of Quicksort algorithms and Divide & Conquer algorithms, respectively. 相似文献
13.
We answer a question of Blumberg, Cohen and Teleman, showing that the Chas–Sullivan loop homology is the Hochschild cohomology of any object in the rational string topology category of a compact, simply connected, Lie group G. Moreover, we show that the answer follows from the classification of the localizing subcategories of the derived category of chains on the based loops of G, which we achieve using the stratification machinery of Benson, Iyengar and Krause. For integral coefficients we get similar results for G a simply-connected special unitary group. 相似文献
14.
Adam J. Prze?dziecki 《Advances in Mathematics》2010,225(4):1893-1913
We construct a functor F:Graphs→Groups which is faithful and “almost” full, in the sense that every nontrivial group homomorphism FX→FY is a composition of an inner automorphism of FY and a homomorphism of the form Ff, for a unique map of graphs f:X→Y. When F is composed with the Eilenberg-Mac Lane space construction K(FX,1) we obtain an embedding of the category of graphs into the unpointed homotopy category which is full up to null-homotopic maps.We provide several applications of this construction to localizations (i.e. idempotent functors); we show that the questions:
- (1)
- Is every orthogonality class reflective?
- (2)
- Is every orthogonality class a small-orthogonality class?
15.
We construct a class of Finsler metrics in three-dimensional space such that all their geodesics are lines, but not all planes are extremal for their Hausdorff area functionals. This shows that if the Hausdorff measure is used as notion of volume on Finsler spaces, then totally geodesic submanifolds are not necessarily minimal, filling results such as those of Ivanov [On two-dimensional minimal fillings, St. Petersburg Math. J. 13 (2002) 17-25] do not hold, and integral-geometric formulas do not exist. On the other hand, using the Holmes-Thompson definition of volume, we prove a general Crofton formula for Finsler spaces and give an easy proof that their totally geodesic hypersurfaces are minimal. 相似文献
16.
A. Liepinš 《Numerical Functional Analysis & Optimization》2013,34(5):387-396
An extension to topological spaces of a wellknown fixed point theorem of M. Edelstein for contractive mappings on metric spaces is presented. Results based on the generalized Edelstein's theorem are also established concerning the existence of fixed points of continuous selfmaps on a topological space. As a special case a compact starshaped subset of a linear topological space is considered. The results extend the fixed point theoremsfor nonexpansive mappings on a compact metric space of L.F.Guseman, Jr. and B.C. Peters, Jr. 相似文献
17.
Mahmoud Benkhalifa 《Journal of Pure and Applied Algebra》2007,210(2):343-362
The present paper is devoted to the classification problem of the quasi-isomorphism classes of free differential graded algebras (dgas) over a (P.I.D) R. We introduce the notion of coherent homomorphisms, perfect and quasi-perfect dgas (the Adams-Hilton model of simply connected CW-complex such that H∗(X,R) is free is a such a dga) and our first main result asserts that two perfect (quasi-perfect) dgas are quasi-isomorphic if and only if their Whitehead exact sequences are coherently isomorphic. Moreover we define the notion of a strong isomorphism between the Whitehead exact sequences and we show that two free R-dgas, of which their Whitehead exact sequences are strongly isomorphic, are quasi-isomorphic. 相似文献
18.
G. I. Chertanov 《Siberian Mathematical Journal》1993,34(6):1180-1189
Tol'yatti. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 6, pp. 198–209, November–December, 1993. 相似文献
19.
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
20.
Luis J. Alías Takashi Kurose Gil Solanes 《Differential Geometry and its Applications》2006,24(5):492-502
We prove that a bounded, complete hypersurface in hyperbolic space with normal curvatures greater than −1 is diffeomorphic to a sphere. The completeness condition is relaxed when the normal curvatures are bounded away from −1. The diffeomorphism is constructed via the Gauss map of some parallel hypersurface. We also give bounds for the total curvature of this parallel hypersurface. 相似文献