If F is a closed set and G is open, show that FG is closed and...

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If F is a closed set and G is open, show that FG is closed and G\ F is open. Let f: RR be continuous. Show that {r: f(x) > 0) is an open subset of R and {r: f(x)=0} is closed in R. If F is a closed set and G is open, show that FG is closed and G\ F is open. Let f: RR be continuous. Show that {r: f(x) > 0) is an open subset of R and {r: f(x)=0} is closed in R.