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alice8675309

Member

Registered: 2010-04-06

Posts: 2

Show that f is bounded in two ways:

Suppose f: K->(-

,

), K is compact, and f has a finite limit at each point of K, but may not be continuous on K. Show that f is bounded in two ways: (i) by using the definition of compactness in terms of open covers, and (ii) by using the sequential characterization of compactness. Is the same conclusion valid if we drop the assumption that the limit of f is finite?