Unformatted text preview: ± f ( x n ) f ( y n )± ≥ ε . Hint : First prove ²⇒ direction for (a) and (b). This automatically implies ⇐² direction for both parts (explain why). 2. Let D = ( a,c ] ∪ [ b,d ) such that a < b and c < d , where d could be ∞ . Let f ∶ D → R and show that if f is uniformly continuous on ( a,c ] and f is uniformly continuous on [ b,d ) , then f is uniformly continuous on the whole D . caution : You have to consider the following cases separately: c < b , c = b and b < c ....
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 Spring '08
 JUNGE
 Math, Calculus, Topology, Continuous function, yn, Uniform continuity, elementary real analysis

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