Modern Dimension Theory |
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Akad Alexandroff assume barycentric subdivisions characterize closed collection closed continuous mapping closed sets closed subset compact metric space compact spaces construct continuous function corollary to Theorem cozero set Definition VIII denote dim R≤n dimension functions dimension theory disjoint closed sets Dokl element Euclidean space exists an open extended F and G F₁ finite closed covering finite open basis finite open covering Fundam Hence homomorphism implies Ind B(V Ind F induction hypothesis inductive dimension infinite-dimensional spaces integer Let f locally finite closed locally finite open mapping f Math Metrization Theorem Morita n-dimensional Nagata obtain open set ordinal number paracompact space positive number Proc Proof proved separable metric space simplex star-finite subspace sum theorem Suppose Theorem VII topological space transfinite inductive U₁ U₂ V₂ weakly infinite-dimensional α α α κα