Topology

A₁ Assume axiom B₁ Baire space bijective c-topology called cardinal cartesian product closed sets compact space completely regular completely regular space connected containing continuous f continuous map converges countably compact d-Cauchy define Definition Let deformation retract denoted dense discrete space element En+1 equivalence relation exists extendable family of sets fiber structure filterbase finite follows function gauge given H-structure Hausdorff space homeomorphism homotopy Hurewicz fibration identity map induced injective intersection inverse isomorphic k-space lemma Let f locally compact map f map ƒ metric space normal open covering open map open sets ordinal number paracompact partially ordered path-connected preordered Proof Prove real numbers satisfies Section sequence subset subspace surjective Theorem Let topological space topology trivial U₁ V₁ vector verify Y₁ α α α