摘要:

The category of all complete distributive lattices and their complete homomorphisms is universal, and this is also true for the category of all complete distributive lattices whose morphisms preserve complete joins, finite meets and an additional nullary operation. A survey of analogous results on algebraic universality of categories based on finitary distributive (0,1)-lattices is included to motivate further questions about categories based on complete distributive lattices.

ISSN:1607-3606    

DOI:10.2989/16073600009485975

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

LetAbe anMV-algebra andIbe an ideal ofA. Let SpecAbe the space of the prime ideals ofAwith the usual hull-kernel topology. LetU(I) = {P∈ SpecA/I⊈P} be open in SpecA.U(I) is stable open iffQ∈ SpecA,P⊆Q,P∈U(I) implyQ∈U(I).Iis said pure iffU(I) is stable open. Like happens in the commutative rings with unit and in the bounded distributive lattices, the pure ideals ofAare characterized via the closed subsets of the hull-kernel topology of MaxA, the space of the maximal ideals ofA. Opens and stable opens of MaxAcoincide. Some classes ofMV-algebras are also described in terms of their pure ideals.

ISSN:1607-3606    

DOI:10.2989/16073600009485976

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

We prove some theorems regarding the set of finite images of certain groups. The groups concerned include some two-generator one-relator groups, as well as (infinite) quotients of such groups. We also prove, by means of cancellation techniques, that certain groups, in the class of all finitely generated groups with finite commutator subgroups, are determined uniquely up to isomorphism in this class, by their finite quotients.

ISSN:1607-3606    

DOI:10.2989/16073600009485977

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

We prove that every 2-summing operator from a Banach spaceXinto anL1-space is nuclear if and only ifXis isomorphic to a Hilbert space. Then we study the class of Banach spacesXfor which Π2(l2,X) =N1(l2,X).

ISSN:1607-3606    

DOI:10.2989/16073600009485978

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Extrinsic and intrinsic characterizations are given for the class DSC(K) of differences of semi-continuous functions on a Polish spaceK, and also decomposition characterizations of DSC(K) and the class PS(K) of pointwise stabilizing functions onKare obtained in terms of behavior restricted to ambiguous sets. The main, extrinsic characterization is given in terms of behavior restricted to some subsets of second category in any closed subset ofK. The concept of a strong continuity point is introduced, using the transfinite oscillations oscαfof a functionfpreviously defined by the second named author. The main intrinsic characterization yields the following DSC analogue of Baire's characterization of first Baire class functions: a function belongs to DSC(K) iff its restriction to any closed non-empty setLhas a strong continuity point. The characterizations yield as a corollary that a locally uniformly converging seriesσϕjof DSC functions onKconverges to a DSC function providedσoscαϕjconverges locally uniformly for all countable ordinalsα.

ISSN:1607-3606    

DOI:10.2989/16073600009485979

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

LetXbe an (E,M)-category for sinks. A recently introduced notion of connectedness with respect to a closure operatorConXand to a class ofX-monomorphismsNis further analyzed. The notion ofN-connectedness hull of a class ofX-objects is introduced and a characterization of it is presented under the assumption ofNbeing closed under the formation of pullbacks. Moreover, a characterization of the related notion ofN-connectedness class is presented under the assumption thatXcontains a terminal object. Some examples are provided.

ISSN:1607-3606    

DOI:10.2989/16073600009485980

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

Assume thatIdenotes the unit interval [0, 1] and BIis theσ-algebra of all Borel subsets ofI. Then any numberx∈Ican be written in a unique way as a continued fraction with odd partial quotients. In this paper we determine a class of probability measures on the measurable space (I, BI) under which the rests of the continued fractions with odd partial quotients are identically distributed random variables.

ISSN:1607-3606    

DOI:10.2989/16073600009485981

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

In this work, we use the extrapolation methods to study the existence and the uniqueness of bounded and almost periodic, asymptotic almost periodic, pseudo almost periodic and Eberlein-weak almost periodic solutions to hyperbolic Cauchy problems for Hille-Yosida operators d/dtx(t) =Ax(t) +f(t),t∈ R, when the inhomogeneitiesftake their values in the extrapolated Favard class corresponding toA.

ISSN:1607-3606    

DOI:10.2989/16073600009485982

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

For any weightable quasi-metric space (X, d) having a maximum with respect to the associated order ≤d, the notion of the quasi-metric of complexity convergence on the the function space (equivalently, the space of sequences)Xω, is introduced and studied. We observe that its induced quasi-uniformity is finer than the quasi-uniformity of pointwise convergence and weaker than the quasi-uniformity of uniform convergence. We show that it coincides with the quasi-uniformity of pointwise convergence if and only if the quasi-metric space (X, d) is bounded and it coincides with the quasi-uniformity of uniform convergence if and only ifXis a singleton. We also investigate completeness of the quasi-metric of complexity convergence. Finally, we obtain versions of the celebrated Grothendieck theorem in this context.

ISSN:1607-3606    

DOI:10.2989/16073600009485983

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor

摘要:

The growth conditions on the powers in the Gelfand-Hille theorems can be replaced by the same conditions on the Cesàro means, retaining the conclusions. Moreover, the assumptions can be further weakened on one of the two sides.

ISSN:1607-3606    

DOI:10.2989/16073600009485984

出版商:Taylor & Francis Group    

年代:2000

数据来源: Taylor