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In this paper, we construct a regular space with a countable network (even the union of countably many separable metric subspaces) in which and do not coincide under the assumption of the continuum hypothesis (CH). This gives a consistent negative answer to a question of A.V. Arhangel'skii.  相似文献   

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We study some topological and metrical properties of configuration spaces. In particular, we introduce a family of metrics on the configuration space Γ, which makes it a Polish space. Compact functions on Γ are also considered. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

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We prove that the moduli space of regular stable maps in a complex manifold admits a natural complex orbifold structure. Our proof is based on Hardy decompositions and Fredholm intersection theory. The authors would like to thank the referee for his/her diligent work. We are grateful for the careful attention to detail in the report.  相似文献   

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Up to now, the only known examples of homogeneous nontrivial Ricci soliton metrics are the so-called solvsolitons, i.e., certain left-invariant metrics on simple connected solvable Lie groups. In this article, we describe the moduli space of solvsolitons of dimension ≤ 6 up to isomorphism and scaling. We start with the already known classification of nilsolitons and, following the characterization given by Lauret in (J. Reine Angew. Math. 650:1–21, 2011), we describe the subspace of solvsolitons associated to a given nilsoliton, as the quotient of a Grassmanian by a finite group.  相似文献   

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Sagdeev  A. A. 《Mathematical Notes》2017,102(3-4):541-546

An explicit exponentially growing lower bound for the chromatic number of Euclidean space with forbidden regular simplex is constructed.

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We consider parabolic systems
$u_{t} - {\rm div} \left( a(t, x, u, \nabla u)\right) + a_{0}(t, x, u, \nabla u) = 0$
in two space dimensions with initial and Dirichlet boundary conditions. The elliptic part including a 0 is derived from a potential with quadratic growth in ?u and is coercive and monotone. The term a 0 may grow quadratically in ?u and satisfies a sign condition a 0 · u ≥ ?K. We prove the existence of a regular long time solution verifying a regularity criterion of Arkhipova. No smallness is assumed on the data.
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Let (R,m) be a Noetherian local ring of depth d and C a semidualizing R-complex. Let M be a finite R-module and t an integer between 0 and d. If the GC-dimension of M/aM is finite for all ideals a generated by an R-regular sequence of length at most dt then either the GC-dimension of M is at most t or C is a dualizing complex. Analogous results for other homological dimensions are also given.  相似文献   

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We establish a relationship between Schreiner's matrix regular operator space and Werner's (nonunital) operator system. For a matrix ordered operator space V with complete norm, we show that V is completely isomorphic and complete order isomorphic to a matrix regular operator space if and only if both V and its dual space V are (nonunital) operator systems.  相似文献   

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If and are Banach lattices such that is separable and has the countable interpolation property, then the space of all continuous regular operators has the Riesz decomposition property. This result is a positive answer to a conjecture posed by A. W. Wickstead.

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A simpler example of regular space that is not completely regular is attempted.  相似文献   

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给出了关于子基的正则空间和相对正则性概念,研究了各种正则性之间的关系,证明了各种正则空间的充要条件,丰富了一般拓扑学中的正则空间和相对正则性理论.  相似文献   

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Supported by NATO collaborative research grant CRG 900029  相似文献   

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We partially solve a well-known conjecture about the nonexistence of positive entire solutions to elliptic systems of Lane-Emden type when the pair of exponents lies below the critical Sobolev hyperbola. Up to now, the conjecture had been proved for radial solutions, or in n?3 space dimensions, or in certain subregions below the critical hyperbola for n?4. We here establish the conjecture in four space dimensions and we obtain a new region of nonexistence for n?5. Our proof is based on a delicate combination involving Rellich-Pohozaev type identities, a comparison property between components via the maximum principle, Sobolev and interpolation inequalities on Sn−1, and feedback and measure arguments. Such Liouville-type nonexistence results have many applications in the study of nonvariational elliptic systems.  相似文献   

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We consider the vector space C(X, E) of all bounded continuous functions from a completely regular space X into a Banach space E. It is given a special locally convex topology . We prove the analog of the Riesz-Markov theorem for the -continuous linear operators which map C (X, E) into a Banach space F.Translated from Matematicheskie Zametki, Vol. 20, No. 3, pp. 401–408, September, 1976.  相似文献   

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