Methods of Commutative Algebra for Topology |
Contents
Introduction | 1 |
Separation conditions | 7 |
The Continuous Retract Theorem | 43 |
Copyright | |
4 other sections not shown
Common terms and phrases
0-dimensional A₁ abelian groups arbitrary basic open set basis for Spec belongs bijection Boolean algebra boundary C₁ C₂ chain of prime closed interval closed point closed sets closed subset closure commutative rings compact Hausdorff space compact space compactification complement completely regular space conclude contains continuous functions continuous map Corollary define Definition denote disjoint neighborhoods distributive lattice dual lattice element exact sequence exists finite spaces finite topological space flabby follows Hence homeomorphism inductive dimension inductive limit intersection irreducible closed sets lattice morphism Lemma Let F lim F locally compact maximal ideal maximal spectrum noetherian space non-empty normal lattice open neighborhoods open set open subset point of Spec principal ideal projective limit projective system Proof set in Spec sheaf of abelian sheaves Spec 1m Spec Ax Spec C(X spectral space Stone space structural map sublattice subspace of Spec supremum surjective T₁-space topological space unique X₁ zero-sets