Dimension Theory (PMS-4), Volume 4Book 4 in the Princeton Mathematical Series. |
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a-mapping arbitrary B₁ barycentric subdivisions basis group bdry bounding Brouwer C₁ C₂ character group closed set closed subset cobounding cocycle cohomology groups compact space complex contained coordinates are rational COROLLARY countable countable sum covering defined Definition VIII denote dense direct system disconnected element Euclidean n-space Example VIII exists extended follows functional space ƒ and g G)-chain G₁ G₂ group G H₂(K H₂(X Hence Hm(K homology and cohomology homomorphism h homotopic implies induced integer interior point intersection inverse system inverse-image isomorphic K₁ K₂ Let G limit group mapping ƒ mapping g Math metric space n-chain n-dimensional space n-sphere natural homomorphism non-empty open set oriented n-simplex p₁ polytope Proposition prove R₁ real number S₂ satisfying sequence set of points simplexes simplicial mapping space of dimension spherical neighborhood subgroup subspace Suppose system of groups Theorem VIII topological U₁ V₁ vertex vertices zero