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Topology of metric spaces by S. Kumaresan

Topology of metric spaces S. Kumaresan ebook
Format: djvu
ISBN: 1842652508, 9781842652503
Page: 162
Publisher: Alpha Science International, Ltd

Topology usually starts with the idea of a *metric space*. The next group is three books which spend a lot of time on proto-topology, as it were. We need to define that first, before we can get into anything really interesting. Abstract: We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is robust to noise and outliers. And also incorporates with his permission numerous exercises from those notes. For my counter example, consider the metric space (0,1), with the usual distance metric. Naive set theory, topological spaces, product spaces, subspaces, continuous functions, connectedness, compactness, countability, separation axioms, metrization, and complete metric spaces. A metric space is a set of values with some concept of *distance*. The volume includes an Appendix that helps bridge the gap between metric and topological spaces, a Selected Bibliography, and an Index. Compactness of (0,1) when that is the whole metric space in Topology and Analysis is being discussed at Physics Forums.