Unformatted text preview: 4111 R N Notes • Theorem 4 ( R N is complete, using previously proved theorems) • Theorem 6 (HeineBorel, again using previously proved theorems) 4111 R ∞ Notes • Theorem 6 (Examples that bounded sets in R ∞ need not be totally bounded) 511 Continuity Notes • Theorem 4 (Equivalence of the εδ and sequence deﬁnitions of continuity) 511 Continuity and Connectedness Notes • Theorem 2 (Intermediate Value Theorem) 4111 Existence of Optima Notes • Theorem 1(the continuous image of a compact set is compact) • Theorem 2 (a continuous realvalued function on a compact set has a maximum)...
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 Fall '08
 JohnNachbar
 Topology, Intermediate Value Theorem, Metric space, Compact space, John Nachbar

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