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Proximity and uniform
Extensions of spaces
5 other sections not shown
according Accordingly arbitrary assign belonging boundary bounded called Cauchy centred clearly closed sets compact compactification condition connected consequence consider consisting constitute constructed containing convergence countable defined definition denoted disjoint distance element equivalent evidently example exercise exists extension fact filter base finally formulated function further Give given hand hence holds identical implies important induced interior intersection interval limit locally metric space neighbourhood base neighbourhood space neighbourhood structure normal notation notion obtained open cover open sets paracompact Proof Prove proximity proximity space pseudo-metric space relation respect satisfies separated sequence Show space E subsets subspace suitable Suppose surrounding system of sets T-open topological space topology true uniform space union