General Topology

Apply base cardinal number Cartesian product Čech-complete closed mapping closed sets closed subsets closed subspace closure compact subspace compact-open topology compactification completely metrizable consider contains continuous function continuous mapping convergence COROLLARY countably compact countably paracompact Deduce defined denoted dense discrete space Exercise exists F}ses finite open first-countable follows function f functionally open G-set Hausdorff space Hence hereditarily Hint homeomorphic implies invariant inverse system Lemma Lindelöf space linearly ordered locally compact space locally finite mapping f mapping ƒ metrizable space natural number neighbourhood non-empty normal space open cover open mapping open refinement open sets open subsets pair paracompact space perfect mapping point xe Problem Proof Proposition Prove pseudocompact pseudometric quotient mapping real line realcompact regular space respect satisfying Section space X ẞX suffices to show T-space topological space topology induced totally bounded Tychonoff space U₁ uniform space V₁ Verify X}ses X₁