Topology

2º countable A₁ Assume axiom B₁ Baire space bijective c-topology called cardinal cartesian product closed map 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 Euclidean exists extendable f₁ fiber structure filterbase finite follows gauge given H-structure Hausdorff space homeomorphism Hurewicz fibration identity map induced intersection isomorphism k-space lemma Let f Lindelöf locally compact map f metric space nonempty normal open covering open map open sets ordinal number paracompact path component path-connected Proof Prove real numbers regular space satisfies Section sequence subbasis subset subspace surjective Theorem Let topological space topology trivial U₁ V₁ verify Vn+1 well-ordered Y₁ α α α αε