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Poiesis and Enchantment in Topological Matter$
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Xin Wei Sha

Print publication date: 2014

Print ISBN-13: 9780262019514

Published to MIT Press Scholarship Online: September 2014

DOI: 10.7551/mitpress/9780262019514.001.0001

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Topology, Manifolds, Dynamical Systems, Measure, and Bundles

Topology, Manifolds, Dynamical Systems, Measure, and Bundles

Chapter:
(p.161) 6 Topology, Manifolds, Dynamical Systems, Measure, and Bundles
Source:
Poiesis and Enchantment in Topological Matter
Author(s):

Xin Wei Sha

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262019514.003.0006

This is the core chapter, introducing concepts that articulate continua, continuous substance, and continuous process. These concepts find precise and deep forms in point set topology, topological and differentiable dynamical systems (qualitative, topological, and geometrical approaches to systems of ordinary differential equations), and the much more sophisticated perspectives of differential geometry and fiber bundles. Basic poetic concepts introduced include: open (closed) set, neighborhood, map, space, continuity, connectedness, limit, convergence, compactness, and so forth. Introducing the work of Brouwer, Thom, and Petitot prepares the reader for a critical encounter with Petitot's program on ontogenesis. Articulating matter with such anexact concepts seeds the ground for an alternative, nonreductionist approach to ontogenesis. Certain terms used in earlier chapters for their intuitive senses, such as continuous, limit, dense, etc., will now be presented more rigorously, so that they can be used with more precise connotations and conceptual purchase after this chapter.

Keywords:   topology, differential geometry, Lie groups, fibre bundles, dynamical system

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