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\centerline{\bf ADVANCED CALCULUS, Math 127 B}
\centerline{\bf Homework 1 Due Friday January 16}
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\item Decide whether $R$ with the following functions as proposed
metrics make up a real metric space: (a) $d(x,y)=|x^2-y^2|$ (b)
$d(x,y)=\frac{|x-y|}{1+|x-y|}$.

\item Let $Q$ be the set of rational numbers with the usual distance
function (e.g $d(x,y)=|x-y|$). Is this a metric space? If yes, 
is the Heine-Borel theorem still true for this? Prove or disprove.

\item Let $F:R^k \rightarrow R$ be a continuous function. Let
$Z(f)=\{p\in R^k | f(p)=0\}$. Prove $Z(f)$ is a closed set.

\item Exercise 21.9

\item Exercise 21.10

\item Exercise 22.1 

\item Exercise 22.6

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