Compactness, Homologies of General Spaces (v. 2) (Encyclopaedia of Mathematical Sciences) - Tapa dura

 
9783540546955: Compactness, Homologies of General Spaces (v. 2) (Encyclopaedia of Mathematical Sciences)
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ISBN 10: 3540546952 ISBN 13: 9783540546955
Editorial: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1995

Sinopsis

This volume consists of two parts. The first contains a survey of results related to the concept of compactness in general topology, highlighting the role that it plays in many areas of general topology. The second is devoted to homology and cohomology theories of general spaces. Special emphasis is placed on the method of sheaf theory as a unified approach to constructions of such theories.

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Reseña del editor

Compactness is related to a number of fundamental concepts of mathemat­ ics. Particularly important are compact Hausdorff spaces or compacta. Com­ pactness appeared in mathematics for the first time as one of the main topo­ logical properties of an interval, a square, a sphere and any closed, bounded subset of a finite dimensional Euclidean space. Once it was realized that pre­ cisely this property was responsible for a series of fundamental facts related to those sets such as boundedness and uniform continuity of continuous func­ tions defined on them, compactness was given an abstract definition in the language of general topology reaching far beyond the class of metric spaces. This immensely extended the realm of application of this concept (including in particular, function spaces of quite general nature). The fact, that general topology provided an adequate language for a description of the concept of compactness and secured a natural medium for its harmonious development is a major credit to this area of mathematics. The final formulation of a general definition of compactness and the creation of the foundations of the theory of compact topological spaces are due to P.S. Aleksandrov and Urysohn (see Aleksandrov and Urysohn (1971)).

Contraportada

This volume of the Encyclopaedia consists of two independent parts. The first contains a survey of results related to the concept of compactness in general topology. It highlights the role that compactness plays in many areas of general topology. The second part is devoted to homology and cohomology theories of general spaces. Special emphasis is placed on the method of sheaf theory as a unified approach to constructions of such theories. Both authors have succeeded in presenting a wealth of material that is of interest to students and researchers in the area of topology. Each part illustrates deep connections between important mathematical concepts. Both parts reflect a certain new way of looking at well known facts by establishing interesting relationships between specialized results belonging to diverse areas of mathematics.

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Editorial
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Año de publicación
1995
Idioma
Inglés
ISBN 10 
3540546952
ISBN 13 
9783540546955
Encuadernación
Tapa dura
Número de páginas
263
Editor
Arkhangel'skii A. V., Arhangelskii A.V.
Contacto del fabricante
no disponible
Persona responsable
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Otras ediciones populares con el mismo título

9783642770326: General Topology II: Compactness, Homologies of General Spaces: 50 (Encyclopaedia of Mathematical Sciences)

Edición Destacada

ISBN 10:  3642770320 ISBN 13:  9783642770326
Editorial: Springer, 2011
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