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Books > Science & Mathematics > Mathematics > Mathematical foundations
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Approach Spaces - The Missing Link in the Topology-Uniformity-Metric Triad (Hardcover)
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Approach Spaces - The Missing Link in the Topology-Uniformity-Metric Triad (Hardcover)
Series: Oxford Mathematical Monographs
Expected to ship within 12 - 17 working days
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In topology the three basic concepts of metrics, topologies and
uniformities have been treated so far as separate entities by means
of different methods and terminology. This work treats all three
concepts as a special case of the concept of approach spaces. This
theory provides an answer to natural questions in the interplay
between topological and metric spaces by introducing a well suited
supercategory of TOP and MET. The theory makes it possible to equip
initial structures of metricizable topological spaces with a
canonical structure, preserving the numerical information of the
metrics. It provides a solid basis for approximation theory,
turning ad hoc notions into canonical concepts, and it unifies
topological and metric notions. The book explains the richness of
approach structures in detail; it provides a comprehensive
explanation of the categorical set-up, develops the basic theory
and provides many examples, displaying links with various areas of
mathematics such as approximation theory, probability theory,
analysis and hyperspace theory. This book is intended for
lecturers, researchers and graduate students in the following
areas: topology, categorical theory, category th
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