Approximate Topologies

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Abstract
Several examples illustrate the utility of mathematical models which differ in their topological properties from the ``real'' systems they describe. The examples are the Aharonov‐Bohm effect, the periodic lattice, and scattering off an obstacle. By going to the approximate topology, the Hamiltonian loses its essential self‐adjointness, but the relation of the approximate to the exact topology leads to a convenient classification of its extensions.