# Continuity

• May 13th 2010, 03:07 PM
janae77
Continuity
Let f be defined and continuous on a closed set S in R. Let A={x: x $\in$S and f(x)=0}.
Prove that A is a closed subset of R .
• May 13th 2010, 03:38 PM
Plato
Quote:

Originally Posted by janae77
Let f be defined and continuous on a closed set S in R. Let A={x: x $\in$S and f(x)=0}.
Prove that A is a closed subset of R .

Hint: If $f$ is continues and $f(p)\not=0$ then there is an open interval such that $p\in (s,t)$ and $f$ is non-zero on $(s,t)$.
Hence, does this show the complement open?