Topology |
Contents
Chapter 0 | 1 |
METRIC SPACES | 47 |
include Exercises 1 85 and 1 | 86 |
Copyright | |
17 other sections not shown
Common terms and phrases
arbitrary Assume basic open set belongs bijection Cauchy sequence Choose closed interval closed subset collection compact Hausdorff space compact space construct contains continuous function continuous map converges Corollary countable d-ball d-bounded d-closed d-open sets d')-continuous d₁ d₂ defined definition denoted dense denumerable discrete space disjoint equivalence relation Euclidean metric example Exercise exists extended real line first-countable function f given Hausdorff space Hence homeomorphic infinite intersection isometry Lemma Let f locally compact map f max metric metric space nonempty open cover open interval open neighborhood open sets open subset positive integer product space product topology Proof Proposition Prove quotient space real line real numbers relative topology S₁ S₂ second-countable subspace Suppose surjection Theorem topological property topological space total ordering U₁ uncountable upper bound usual topology X₁ Xn+1