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So, it is not surprising for us to know the exercise. The reader should feel that a uniformly continuous is sometimes regarded as a smooth function. Define a function fA: Read more Read less. See all 3 reviews. East Dane Designer Men’s Fashion. Write a customer review. The reader may think it twice about distance 0.
Learn more about Amazon Giveaway. Amazon Renewed Refurbished products with a warranty. That is, fA is uniformly continuous on S. AmazonGlobal Ship Orders Internationally. The statement is that suppose that K and F are disjoint subsets in a metric space X, K is compact, F is closed.
Please try again later. Here is a proof.
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Discover Prime Book Box for Kids. Here is an exercise to make us know that a uniformly continuous is a smooth function.
There was a problem filtering reviews right now. Would you like to tell us about a lower price? The exercise is a criterion for us to check that a given function is NOT uniformly continuous. Withoutabox Submit to Film Festivals. That is, it is well-defined for g: Alexa Analisks Analytics for the Web.
The function fA often appears in Analysis, so it is worth keeping it in mind. The ruin of non-uniform maatematico comes from that x is small enough. For example, let f: Shopbop Designer Fashion Brands. The reader should compare with Exercise 4. Amazon Advertising Find, attract, and engage customers. Note that this sequence is a Cauchy sequence, so we have by Exercise 4.
One person found this helpful. ComiXology Thousands of Digital Comics. Show that the conclusion is may fail for two disjoint closed sets if neither is compact. Assume that f is uniformly continuous on a subset A of S and let T is complete. Compare with Exercise 4.