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We prove a Dichotomy Theorem: for any Hausdorff compactification bG of an arbitrary rectifiable space G, the remainder bG?G is either pseudocompact or Lindelöf. This theorem generalizes a similar theorem on topological groups obtained earlier in A.V. Arhangel'skii (2008) [6], but the proof for rectifiable spaces is considerably more involved than in the case of topological groups. It follows that if a remainder of a rectifiable space G is paracompact or Dieudonné complete, then the remainder is Lindelöf and that G is a p-space. We also present an example showing that the Dichotomy Theorem does not extend to all paratopological groups. Some other results are obtained, and some open questions are formulated. 相似文献
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A.V. Arhangel'skii 《Topology and its Applications》2005,150(1-3):79-90
When does a Tychonoff space X have a Hausdorff compactification with the remainder belonging to a given class of spaces? A classical theorem of Henriksen and Isbell and certain theorems, involving a new completeness type property introduced below, are applied to obtain new results on remainders of topological spaces and groups. In particular, some strong necessary conditions for a topological group to have a metrizable remainder, or a paracompact p-remainder, are established (the group itself turns out to be a paracompact p-space (Theorem 4.8)). It follows that if a non-locally compact topological group G is metrizable at infinity, then G is a Lindelöf p-space, and the Souslin number of G is countable (Corollary 4.10). This solves Problem 10.28 from [M. Hušek, J. van Mill (Eds.), Recent Progress in General Topology, vol. 2, North-Holland, 2002, pp. 1–57]. 相似文献
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Abstract polytopes are combinatorial and geometrical structures with a distinctive topological flavor, which resemble the
convex polytopes. C-groups are generalizations of Coxeter groups and are the automorphism groups of abstract polytopes which
are regular. We investigate general properties of quotients of abstract polytopes and C-groups.
Supported by NSF Grant DMS-9202071. 相似文献
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A Bing space is a compact Hausdorff space whose every component is a hereditarily indecomposable continuum. We investigate spaces which are quotients of a Bing space by means of a map which is injective on components. We show that the class of such spaces does not include every compact space, but does properly include the class of compact metric spaces. 相似文献
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Evan P. Wright 《Annals of Global Analysis and Geometry》2012,41(1):91-108
A classification result for Ricci-flat anti-self-dual asymptotically locally Euclidean 4-manifolds is obtained: they are either
hyperk?hler (one of the gravitational instantons classified by Kronheimer), or they are a cyclic quotient of a Gibbons–Hawking
space. The possible quotients are described in terms of the monopole set in
\mathbbR3{\mathbb{R}^3} , and it is proved that every such quotient is actually K?hler. The fact that the Gibbons–Hawking spaces are the only gravitational
instantons to admit isometric quotients is proved by examining the possible fundamental groups at infinity: most can be ruled
out by the classification of three-dimensional spherical space form groups, and the rest are excluded by a computation of
the Rohklin invariant (in one case) or the eta invariant (in the remaining family of cases) of the corresponding space forms. 相似文献
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Matej Brešar 《Algebras and Representation Theory》2016,19(6):1437-1450
The fundamental theorem on functional identities states that a prime ring R with \(\deg (R)\ge d\) is a d-free subset of its maximal left ring of quotients Q m l (R). We consider the question whether the same conclusion holds for symmetric rings of quotients. This indeed turns out to be the case for the maximal symmetric ring of quotients Q m s (R), but not for the symmetric Martindale ring of quotients Q s (R). We show, however, that if the maps from the basic functional identities have their ranges in R, then the maps from their standard solutions have their ranges in Q s (R). We actually prove a more general theorem which implies both aforementioned results. Its proof is somewhat shorter and more compact than the standard proof used for establishing d-freeness in various situations. 相似文献
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M. I. Hartley 《Discrete and Computational Geometry》1999,21(2):289-298
In this paper it is shown that any (abstract) polytope is a quotient of a regular polytope by some subgroup N of the automorphism group W of , and also that isomorphic polytopes are quotients of by conjugate subgroups of W . This extends work published in 1980 by Kato, who proved these results for a restricted class of polytopes which he called ``regular'. The methods used here are more elementary, and treat the problem in a purely nongeometric manner. Received January 27, 1997, and in revised form October 1, 1997. 相似文献
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Chuan Liu 《Topology and its Applications》2009,156(5):849-854
In this paper, we consider the following question: when does a topological group G have a Hausdorff compactification bG with a remainder belonging to a given class of spaces? We extend the results of A.V. Arhangel'skii by showing that if a remainder of a non-locally compact topological group G has a countable open point-network or a locally Gδ-diagonal, then G and the compactification bG of G are separable and metrizable. 相似文献
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Conrad Plaut 《Topology and its Applications》2006,153(14):2430-2444
This paper develops the basic theory of quotients of uniform spaces via sufficiently nice group actions. We generalize and unify two fundamental constructions: quotients of topological groups via closed normal subgroups and quotients of metric spaces via actions by isometries. Basic results about inverse limits of topological groups are extended to inverse limits of group actions on uniform spaces, and notions of prodiscrete action and generalized covering map are introduced. 相似文献
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Claus Scheiderer 《Mathematische Zeitschrift》1989,201(2):249-271
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Richard P. Stanley 《Order》1984,1(1):29-34
An elementary, self-contained proof of a result of Pouzet and Rosenberg and of Harper is given. This result states that the quotient of certain posets (called unitary Peck) by a finite group of automorphisms retains some nice properties, including the Sperner property. Examples of unitary Peck posets are given, and the techniques developed here are used to prove a result of Lovász on the edge-reconstruction conjecture.Supported in part by a National Science Foundation research grant. 相似文献
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The GIT chamber decomposition arising from a subtorus action on a polarized quasiprojective toric variety is a polyhedral
complex. Denote by Σ the fan that is the cone over the polyhedral complex. In this paper we show that the toric variety defined
by the fan Σ is the normalization of the toric Chow quotient of a closely related affine toric variety by a complementary
torus. 相似文献