For compact $Y$, every open set containing the slice $\ts{x_0}\times Y$ contains a tube $W\times Y$ with $W$ a neighborhood of $x_0$.Suggest a slogan
Let \(X, Y\) be topological spaces with \(Y\) compact, and let \(x_0\in X\). If \(N\subseteq X\cross Y\) is an open set containing the slice \(\theset{x_0} \cross Y\), then there is a neighborhood \(W\) of \(x_0\) in \(X\) with \(W\cross Y\subseteq N\) [@Mun00].
