Chapter VI Nets of Complexes

Book Id: WPLBN0000673344
Format Type: PDF eBook
File Size: 3.31 MB
Reproduction Date: 2005

Title:	Chapter VI Nets of Complexes
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Language:	English
Subject:	Science., Mathematics, Logic
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Citation APA MLA Chicago Chapter VI Nets of Complexes. (n.d.). Chapter VI Nets of Complexes. Retrieved from http://gutenberg.us/

Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: The passage from finite complexes to infinite complexes or topological spaces necessitates some limiting process, and the theory of nets will provide the necessary mechanism. In its general form it may be viewed as abstracted from the tech homology theory for topological spaces (Cech [a]), which will be adopted as the basic theory in (VII). An important special type of net, the sequential spectrum, was already utilized by Alexandroff [a], for compact a, likewise for infinite complexes and compact a in [L, VII]. A close parallel will be found between nets and finite complexes and we shall have here also open and closed subnets, their projections and injections. In the general net there are no chains and so the operations bear directly upon the cycles. However for a spectrum chains may again be introduced, the similarity with complexes being greatly increased thereby.