Asymptotic topology
Copyright policy )Asymptotic topology
We establish some basic theorems in dimension theory and absolute extensor theory in the coarse category of metric spaces. Some of the statements in this category can be translated in general topology language by applying the Higson corona functor. The relation of problems and results of this `Asymptotic Topology' to Novikov and similar conjectures is discussed.
38 pages, AMSTeX
- University of Florida United States
asymptotic category, asymptotically Lipschitz maps, asymptotic dimension, Baum-Connes conjecture, 54F45, 55N15, General Topology (math.GN), asymptotic topology, Higson corona, Categories of topological spaces and continuous mappings, Dimension theory in general topology, Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties), Extensions of spaces (compactifications, supercompactifications, completions, etc.), Novikov conjecture, Metric spaces, metrizability, FOS: Mathematics, Remainders in general topology, absolute extensor, Special maps on metric spaces, Mathematics - General Topology
asymptotic category, asymptotically Lipschitz maps, asymptotic dimension, Baum-Connes conjecture, 54F45, 55N15, General Topology (math.GN), asymptotic topology, Higson corona, Categories of topological spaces and continuous mappings, Dimension theory in general topology, Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties), Extensions of spaces (compactifications, supercompactifications, completions, etc.), Novikov conjecture, Metric spaces, metrizability, FOS: Mathematics, Remainders in general topology, absolute extensor, Special maps on metric spaces, Mathematics - General Topology
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