Inverse Spectra

Volume 53

By: A. Chigogidze

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Hardcover | 29 March 1996

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432 Pages

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23.5 x 16.51 x 2.54

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This is a comprehensive introduction into the method of inverse spectra - a powerful method successfully employed in various branches of topology.

The notion of an inverse sequence and its limits, first appeared in the well-known memoir by Alexandrov where a special case of inverse spectra - the so-called projective spectra - were considered. The concept of an inverse spectrum in its present form was first introduced by Lefschetz. Meanwhile, Freudental, had introduced the notion of a morphism of inverse spectra. The foundations of the entire method of inverse spectra were laid down in these basic works.

Subsequently, inverse spectra began to be widely studied and applied, not only in the various major branches of topology, but also in functional analysis and algebra. This is not surprising considering the categorical nature of inverse spectra and the extraordinary power of the related techniques.

Updated surveys (including proofs of several statements) of the Hilbert cube and Hilbert space manifold theories are included in the book. Recent developments of the Menger and Nöbeling manifold theories are also presented.

This work significantly extends and updates the author's previously published book and has been completely rewritten in order to incorporate new developments in the field.

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Preface
Inverse Spectra
Preliminary information
Definitions and elementary properties of inverse spectra
Factorizing spectra and the spectral theorem
Infinite-Dimensional Manifolds
Absolute extensors and absolute retracts
Z-sets in AN R-spaces
R ohgr; - and I ohgr; -manifolds
Topology of R ohgr; - and I ohgr; -manifolds
Incomplete manifolds
Cohomological Dimension
Cohomological dimension
Cell-like mappings raising dimension
Universal space for cohomological dimension
Menger Manifolds
General theory
n-soft mappings of compacta, raising dimension
n-soft mappings of Polish spaces, raising dimension
Further properties of Menger manifolds
Homeomorphism groups
ohgr;-soft map of sgr; onto Sgr;
Nouml;beling Manifolds
Strongly A ohgr;,n -universal spaces
Pseudo-interiors and pseuod-boundaries of Menger compacta
Geometric pseudo-boundaries
Equivalence of categorical and geometric pseudo-interiors
Equivalence of the Nouml;beling space and the pseudo-interior of mgr; n
Further properties of Nouml;beling spaces
Open subspaces of Nouml;beling spaces
General Theory of Absolute Extensors in Dimension n and n-soft Mappings
AN E(n)-spaces and n-soft mappings
Morphisms of spectra and square diagrams
Spectral characterizations of n-soft mappings
Further properties of AE(0)-spaces
Strongly universal spaces
Topology of Non-Metrizable Manifolds
Non-metrizable manifolds
Topological characterization of I tgr; -manifolds
Topological characterization of R tgr; -manifolds
Trivial bundles
Applications
Uncountable powers of countable discrete spaces
Spectral representations of topological groups
Locally convex linear topological spaces
Shape properties of non-metrizable compacta
Fixed point sets of Tychonov cubes
Compact groups and fixed point sets
Group actions
Baire isomorphisms
Double spectra
Skeletoids in Tychonov cubes
Bibliography
Subject Index
Table of Contents provided by Publisher. All Rights Reserved.

Inverse Spectra

Volume 53

At a Glance

Hardcover

Shipping

How to return your order

Defective items

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