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Metric constructions of topological invariants

Weiss, Ittay (2016) Metric constructions of topological invariants. Topology Proceedings , 49 . pp. 85-104. ISSN 0146-4124

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We present a general mechanism for obtaining topological invari-ants from metric constructs. In more detail, we describe a process which, undervery mild conditions, produces topological invariants out of a construction ona metric space together with a choice of scale (a non-negative value at eachpoint of the space). Through Flagg’s metric formalism of topology the resultsare valid for all topological spaces, not just the metrizable ones. We phrasethe result in much greater generality than required for the topological appli-cations, using the language of fibrations. We show that ordinary topologicalconnectedness arises metrically, and we obtain metrically defined theories ofhomology and of homotopy.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science, Technology and Environment (FSTE)
Depositing User: Ittay Weiss
Date Deposited: 21 Apr 2016 22:39
Last Modified: 03 Mar 2019 23:48

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