摘要:

A detailed study is made of the contravariant functor D which assigns to each compact Hausdorff space X the bounded distributive lattice DX of all functions on X with values in the unit interval, and of some variants of D. In particular, D is shown to have a left inverse, and a duality for compact Hausdorff spaces is derived from D.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632288

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The concept of a biframe is introduced. Then the known dual adjunction between topological spaces and frames (i.e. local lattices) is extended to one between bispaces (i.e. bitopological spaces) and biframes. The largest duality contained in this dual adjunction defines the sober bispaces, which are also characterized in terms of the sober spaces. The topological and the frame-theoretic concepts of regularity, complete regularity and compactness are extended to bispaces and biframes respectively. For the bispaces these concepts are found to coincide with those introduced earlier by J.C. Kelly, E.P. Lane, S. Salbany and others. The Stone-Čech compactification (compact regular coreflection) of a biframe is constructed without the Axiom of Choice.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632289

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

It is shown that the Alexander cohomology groups for merotopic spaces satisfy certain variants of the Eilenberg—Steenrod axioms for a cohomology theory. Furthermore, for a nearness space, the homology and cohomology groups coincide with the corresponding groups of its completion.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632290

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Ind-affine schemes over an algebraically closed field k are introduced. The cone functor is then defined and characterized in the based category (ind-aff)* of ind-affine schemes. Homotopy theories, one induced from the monad related to the cone functor and the other via unirational and then singular simplices, are compared. Some homotopy groups vis-a-vis (ind-aff)* taking as our model of the circle the set of points (x,y) in k2satisfying x2+y2= 1 are determined.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632291

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Let K:P→Tbe a fixed functor. A criterion is given for a functor M':T→Vto be a (right) Kan extension along K of some functor M:P→V.The functors M having a given M' as Kan extension are, in general, classified by continuous functors (VP)o→V.We introduce a notion of system of imprimitivity, generalizing that of Mackey; when the shape category of K is codense in the systems of imprimitivity classify the functors H having M' as Kan extension. As a special case one obtains Mackey's Imprimitivity Theorem for finite groups.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632292

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The Alexandroff (= zero-set) spaces were introduced in [l] as the “completely normal spaces”, and have been studied in a number of more recent papers. In this paper we unify the theory of Wallman realcompactifications via the Alexandroff bases and introduce the realcompactfine Alexandroff spaces as particularly relevant to their investigation. These latter spaces are defined analogously to the A-c uniform spaces which are based on a construction of A.W. Hager [25].

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632293

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Dense subcategories were introduced by S. Mardešić for an inverse system approach to (categorical) shape theory.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632294

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A new treatment is given of the cylinder-web diagram and associated diagonal sequences in homotopy pair theory. The efficiency of the diagram as a machine for computing homotopy pair groups is enhanced by a result that traces the path of a Toda bracket element through the arrows of the diagram. The diagonal factorization problem for a homotopy pair class is studied and related to the behaviour of Toda brackets. A necessary and sufficient condition for the vanishing of a Toda bracket is obtained.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632295

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A generalized Mayer-Vietoris sequence involving crossed homomorphisms is established and the construction is applied to the homotopy sequence of the CW-pair (X.X1) to relate the homotopy sequences of (X.X1) and the fibre bundle F → E → X in low dimensions. If there is a partial cross-section of E → X over X2, the classical form, π1E ∼ π1[xtilde] π1F as a semidirect product, results. In case there is no extension over X2of any cross-section of the restricted bundle χ:π2(x2, x1) → X1the corresponding obstruction map XE:π2(x2,x1) → π1F is non-trivial and in case F → E → X is an SO(n)-bundle (n ≥ 3), χEmaps into a subgroup of the centre, Z(π1F), of order at most 2.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632296

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

We study the question of what properties of nilpotent groups are shared by their abelianizations. We identify two such properties—that of being a π-torsion group, where π is a family of primes, and that of having qthroots, for some prime q. We use these properties to provide simplified proofs of the following theorems in the localization of nilpotent groups.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632297

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor