A non-closed subspace of a topological space is singularly defective, particularly if the topology determines geometric structure. We therefore present completeness as a property of universal closure, confining our attention to metric spaces. We shall see that extraordinarily powerful theorems are available in a metric space which contains every possible boundary point in every possible metric superspace.
KeywordsHilbert Space Banach Space Banach Algebra Cauchy Sequence Division Algebra
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