By
A. Chigogidze, University of Saskatchewan, Department of Mathematics & Statistics, McLean Hall, Saskatoon, Canada
Description
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.
Included in series
North-Holland Mathematical Library
