摘要:

Every topological category over an arbitrary base categoryXmay be considered as a category of T-models with respect to some theory (i.e., functor)TfromXinto a category of complete lattices. Using this model-theoretic correspondence as our basic tool, we study initial and final completions of (co)fibration complete categories. For an arbitrary concrete category (A, U) overX, the process of order-theoretically completing each fibre does not usually yield an initial/final completion of (A, U). It is shown in this paper that for concrete categories which are assumed to be fibration and/or cofibration complete, initial and final completions can be constructed by completing the fibres. These completions are further shown to exhibit some interesting external properties.

ISSN:1607-3606    

DOI:10.1080/16073606.1991.9631642

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

LetRbe a right invariant ring and letS(R) be the lattice of all semiprime ideals ofR.Let κ be an infinite cardinal. It is proved thatS(R) is an algebraic lattice in which the κ-compact elements constitute a sublattice. It follows thatS(R) is isomorphic to the congruence lattice of a lattice.

ISSN:1607-3606    

DOI:10.1080/16073606.1991.9631643

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

There is a close relationship that exists between Lipschitz extensions and best approximations. It is shown that for any function that satisfies the Lipschitz condition on a subset of a metric space (X, d) there always exists a best approximation in the subspace

ISSN:1607-3606    

DOI:10.1080/16073606.1991.9631644

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Results are obtained on the additive groups of semi-local rings. Conditions are given for embedding a ring into a local ring.

ISSN:1607-3606    

DOI:10.1080/16073606.1991.9631645

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

It has recently been shown by Leach and Gorringe that the equation of motionis invariant under the action of the symmetryG=t∂/∂t + αr∂/∂rin addition to the usual time and rotation symmetries in contrast to the occurrence of two extra symmetries for the charge monopole problem (Moreira et al, J Phys, 18 (1985) L427). The integrals associated withGare calculated and an interesting connection with Hamilton-Jacobi theory demonstrated.

ISSN:1607-3606    

DOI:10.1080/16073606.1991.9631646

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Most homotopies considered in the literature are linear homotopies of the formhi(λ) = λxi+ (1—λ)yi, 0 ≤ λ ≤ 1. Although these prove to be adequate in most instances, they lack direct geometric significance because {hi(λ) | 0 ≤ λ ≤ 1} are not orbits of a vector field. On the other hand, the nonlinear homotopygi(s) =esxi+ (1—es)yi,—∞ ≤s≤ 0, are orbits of a vector field (i.e.,dgi/ds=gi—yi,gi(0) =xi), and thus have direct geometric significance. This suggests that useful results can be obtained by replacing linear homotopy by transport along flows of smooth vector fields. The purpose of this paper is to elaborate on this simple idea. We define prehomotopy operators induced by vector fields on a manifold. These allow us to obtain finite transport relations and pre-Poincaré lemmas that generalize the classical results. They are shown to reproduce the classical results as asymptotic limits and to obtain representations of all solutions of complete systems of exterior differential equations on a star shaped region of a manifold.

ISSN:1607-3606    

DOI:10.1080/16073606.1991.9631647

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Definitions of normality and separability for unitary commutative ring extensions are given from the perspective of algebraic and transcendental ring extensions. Necessary and sufficient conditions are given for the set of subringsTi,R⊆Ti⊆S, in a normal separable extensionS:Rin which the extensionsS:Tiare normal separable extensions, to map uniquely bijectively on the set of all subgroups of the Galois group ofS:R.

ISSN:1607-3606    

DOI:10.1080/16073606.1991.9631648

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Several well-known generalizations of the usual topological To-axiom to topological categories are compared. It is shown that they lead to two different concepts: Toand separatedness. The resulting sub-categories are characterized for some important categories of convergence spaces. They provide natural examples disproving the equivalence of the two concepts. Necessary and sufficient conditions are given for the To-objects and separated objects to coincide.

ISSN:1607-3606    

DOI:10.1080/16073606.1991.9631649

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

Spectral theory for the Bessel polynomialsyn(x), which are polynomial solutions of

ISSN:1607-3606    

DOI:10.1080/16073606.1991.9631650

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor

摘要:

LetW(x)= e-Q(z)whereQ(x)is even, continuous on ℝ and of slower than polynomial growth at infinity. We establish, under certain conditions onQ,nth root asymptotics for the extremal error associated withW, Enp(W), 0 < p ≤ ∞ where

ISSN:1607-3606    

DOI:10.1080/16073606.1991.9631651

出版商:Taylor & Francis Group    

年代:1991

数据来源: Taylor