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Set theory and metric spaces by Irving Kaplansky

Set theory and metric spaces Irving Kaplansky ebook
Format: djvu
Page: 154
Publisher: Chelsea Pub Co
ISBN: 0828402981, 9780828402989

In enriched category theory; Examples. F_{F_2}( n) Hyperbolic Metric Spaces. Aug 29 2010 Published by MarkCC under topology. One of the things that topologists like to say is that a topological set is just a set with some structure. Naive set theory, topological spaces, product spaces, subspaces, continuous functions, connectedness, compactness, countability, separation axioms, metrization, and complete metric spaces. We want a notion of metric spaces (and hence for groups) that captures hyperbolicity (that is, for one, that triangles are thin). This is a quasi-isometric invariant of \Gamma . In what follows, X is always a geodesic metric space. Given a set X , we say X is a metric space if it comes equipped with a special function d(x,y) that can compute the distance between any two points x,y of X . One should note that there are even more general spaces that allow for metrics with the triangle inequality, but these usually involve measure theory or take the triangle inequality as an axiom. Specifically, d must satisfy the axioms of a metric. Where B(1, n) is the set of elements \gamma \in \Gamma such that l_S(\gamma) \leq n . In terms of splitting of idempotents; In terms of tiny objects; In terms of absolute colimits; In terms of profunctors; In terms of essential geometric morphisms.