Foundations of Vietoris Homology Theory with Applications to Non-compact Spaces |
Contents
Preface | 5 |
Simple chains | 12 |
Functions mappings and null translations | 25 |
Copyright | |
2 other sections not shown
Common terms and phrases
abelian group abstract n-dimensional Alexandroff equivalence algebraic topology Borsuk boundary operator carrier Xo Čech Čech homology closed locally compact closed subspace compact metric space compact set compact set Xo compact subset compactly dimensioned d₁ define a function denoted dimension theorem dimensional metric space ɛ-chain finite dimensional metric function f ƒ and g hence homomorphism f homotopy theorem ie Ñ induces a homomorphism infinite chain infinite cycle isomorphic lemma let ne Ž locally compact subspaces locally countable union Math Moreover Ñ Ñ null translation numbers Proof proved quotient group satisfies the Alexandroff sequence sequential chains simple chains simplex space with dim spaces and let t₁ Theorem 30 Theorem 42 topological space topology translation with majorant true cycle union of locally vertices Vietoris homology groups Vietoris homology theory Vietoris theory X₁ Y₁ ye Z X Z₁ σ₁