blob: comparison text/blobdef.tex

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 \begin{example}
 Consider the four subsets of $\Real^3$,
 \begin{align*}
 A & = [0,1] \times [0,1] \times [-1,1] \\
 B & = [0,1] \times [-1,0] \times [-1,1] \\
-C & = [-1,0] \times \setc{(y,z)}{z \sin(1/z) \leq y \leq 1, z \in [-1,1]} \\
+C & = [-1,0] \times \setc{(y,z)}{z^2 \sin(1/z) \leq y \leq 1, z \in [-1,1]} \\
-D & = [-1,0] \times \setc{(y,z)}{-1 \leq y \leq z \sin(1/z), z \in [-1,1]}.
+D & = [-1,0] \times \setc{(y,z)}{-1 \leq y \leq z^2 \sin(1/z), z \in [-1,1]}.
 \end{align*}
 Here $A \cup B = [0,1] \times [-1,1] \times [-1,1]$ and $C \cup D = [-1,0] \times [-1,1] \times [-1,1]$. Now, $\{A\}$ is a valid configuration of blobs in $A \cup B$, and $\{C\}$ is a valid configuration of blobs in $C \cup D$, so we must allow $\{A, C\}$ as a configuration of blobs in $[-1,1]^3$. Note however that the complement is not a manifold.
 \end{example}
 \begin{defn}