摘要:

Let Cbe a category of topological spaces and continuous functions which is full, hereditary and closed under homeomorphisms and products. IfAis a subclass ofC, letE(A)be the full subcategory ofCwhose objects are the subspaces inA. In this paper we characterize the epireflective subcategories ofCcontainingAand contained inE(A)by introducing a “semiclosure” operator which is a generalization for the “idempotent semi-limit” operator introduced by S.S. Hong (see [5]) with respect toTopo. In caseAis extensive inC, so thatE(A)=C, all the extensive subcategories ofCcontainingAare thus characterized.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632308

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

This paper deals with projectives (in the sense of K.A.Hardie [5] relative to a right adjoint functor U: A → K. We answer the question, raised by R.-E. Hoffmann [6] p. 135, of knowing under what conditions there exists an equivalence between Proj u and Proj Ur, induced by the comparison functor Φ: A → KT, where T denotes the monad induced by U. In the case, that U is an algebraic functor we also give necessary and sufficient conditions for the re gular projective objects to coincide with the U-projectives. Finally, we delineate how these results nay be applied in certain familiar situations.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632309

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632310

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632311

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

It is proven that, in general, the free algebras of an equational class, considered as an abstract category, are not definable strictly in the language of categories. As a concrete counterexample, a categorical equivalence between the categories of 2-rings and 3-rings is constructed without the axiom of choice. Isomorphism follows, as well as the non-correspondence of free algebras. An assortment of similar negative results and two open questions close the paper.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632312

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Let (T,μ) be a complete measurable space, u a Suslin space and B(u) the Borel σ-algebra of u. The projection theorem, see for example [3], p. 75, states that if the set A belongs to the σ-algebra generated by the class μ x B(U), then its projection PT(A) belongs to the σ-algebra μ. The aim of this note is to show that the projection theorem fails if (T,μ) is incomplete.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632313

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

In this paper two ordered families of topological categories are studied. The first family includes the category of all abstract simplicial complexes and the subcategories of all abstract simplicial complexes of dimension less than or equal to n. The categories of the second family are bireflective subcategories of the category of all bornological spaces. All these categories are cartesian closed and have other nice properties.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632314

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

It is assumed that an n-dimensional distribution is given on an (n+M)-dimensional product space. The latter is endowed with a connection, by means of which the covariant exterior derivatives of the functions that specify the distribution are defined. It is postulated that the connection be such that these derivatives vanish identically. This gives rise to an analysis of the integrability conditions associated with the distribution in terms of appropriate torsion and curvature 2-forms. A further specialization of the connection leads to Edelen's theory [1] of distributions on spaces of fibres.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632315

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632316

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632307

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor