ISSN:1607-3606    

DOI:10.1080/16073606.1977.9632551

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The relationship between Wallman's construction of a compact T1-space [9] and Flachsmeyer's inverse limit spaces of inverse systems of decomposition spaces [2] is investigated. There are connections between Wallman spaces and inverse limits, which were initiated by Alexandroff in 1928. Some old theorems using inverse limits have shorter proofs now. On the other hand we obtain a new method to treat Wallman compactifications in terms of inverse limit spaces. A suitable notion in this context is the “prime-filter space”, having an interesting maximality property. This space seems to be proper to examine prime ideals in C(X).

ISSN:1607-3606    

DOI:10.1080/16073606.1977.9632552

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

First a general Galois correspondence is established, which generalizes at the same time the correspondence between classes of monomorphisms and injective objects and the correspondence between classes of epimorphisms and monomorphisms in a category. This correspondence arises naturally if one tries to generalize some concepts of “topological” or also of “algebraic” functors. Both kinds of functors admit certain factorizations of cones, and just this fact implies some of their common nice properties: lifting limits, continuity and faithfulness, for instance. These properties can be shown without having a left adjoint. Therefore the theory yields also applications to functors which are neither “topological” nor “algebraic”.

ISSN:1607-3606    

DOI:10.1080/16073606.1977.9632553

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

This paper is a survey of recent (and some not so recent, results concerning categorical constructions on topological groups, with particular emphasis on free topological groups and coproducts (free products) of topological groups. An extensive bibliography is included.

ISSN:1607-3606    

DOI:10.1080/16073606.1977.9632554

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

The framework in which nearness spaces were defined by H. Herrlich [1] and [2], leads one to consider the supercategory Pow of the category Near of nearness spaces, having as objects all pairs (X,ξ), where X is a set and ξ ⊂ P(P(X)) is any subset of the power set of the power set of X, and as morphisms f: (X,ξ) → (Y,n) all functions f: X → Y such that, if A ϵ ξ then fA □ {f(A) | A ξ A} ϵ η. In this paper we show that the full subcategories of Pow comprising the objects satisfying subsets of the prenearness space axioms lie in a lattice of bireflections or bicoreflections. This serves as a first step towards the aim of characterizing all bireflective (resp. bicoreflective) and even all initially complete subcategories of Pow.

ISSN:1607-3606    

DOI:10.1080/16073606.1977.9632555

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

John Mather has proved that infinitesimal stability implies stability for proper maps in the category of smooth manifolds. This result gives a computable algebraic criterion for stability. In this paper it is shown that there is an extension of Mather's result when the range is only assumed to be a compact semianalytic set of some real Euclidean space—this class of spaces is an obvious maximal candidate for which computations can be carried out using only classical polynomial algebra. The proof depends on a splitting theorem for the restriction map from the smooth functions on a Euclidean space to those on a closed subset and is proved by an algebraic-geometric method derived from the work of B. Malgrange. No knowledge of functional analysis is assumed although an alternative analytic method for proving the main result is also indicated. Only simple applications are given (mostly to functions defined locally in the neighbourhood of an isolated hypersurface singularity of the type studied by J. Milnor and others) since the author intends to publish a fairly comprehensive study of stability (smooth and C°) of smooth maps on closed semianalytic sets.

ISSN:1607-3606    

DOI:10.1080/16073606.1977.9632556

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

Given a mapping f: X → Y and an extension e: X → [Xtilde] of X, the restriction of the projection Π: [Xtilde] X Y → Y to the closure of the graph of f in [Xtilde] X Y is called the graphic extension of f with respect to e. It is shown that this approach is widely applicable to various types of topological extensions of mappings found in the literature and often gives simpler proofs of their existence, properties, and results relating to them.

ISSN:1607-3606    

DOI:10.1080/16073606.1977.9632557

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

摘要:

We present a homotopy theory of small categories. In a work of this nature there is a need to give a theory which is clear and which shows the methods of work in this field. It is also necessary to prove theorems which place the theory within the general framework of homotopy, i.e. particularly to liaise with the homotopy of topological spaces and with abstract homotopy theories. Firstly we define the important notion of finite functor on which the theory is based. Next we introduce a type of fibred category fitting to the work on homotopy. After having studied the paths and loops of a category, we consider homotopy between functors. Finally, we demonstrate the possibility of obtaining homotopy groups before taking into consideration the relations between categorical and topological homotopy.

ISSN:1607-3606    

DOI:10.1080/16073606.1977.9632558

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1977.9632559

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1977.9632530

出版商:Taylor & Francis Group    

年代:1977

数据来源: Taylor