Exercise 4.3.12. Let F CR be a nonempty closed set and define g(x) inf{|x – a| : a E F}. Show that g is continuous on all of R and g(x) # 0 for all a ¢ F.

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Exercise 4.3.12. Let F CR be a nonempty closed set and define g(x) =
inf{|x – a| : a € F}. Show that g is continuous on all of R and g(x) ± 0 for
all x ¢ F.
Transcribed Image Text:Exercise 4.3.12. Let F CR be a nonempty closed set and define g(x) = inf{|x – a| : a € F}. Show that g is continuous on all of R and g(x) ± 0 for all x ¢ F.
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