Munkres Topology Solutions Chapter 5 -
The Stone–ˇCech Compactification - Central Michigan University
Let $X$ be a compact space, $Y$ any space, and $x_0 \in X$. If $N$ is an open set in $X \times Y$ containing the slice $x_0 \times Y$, then there exists a neighborhood $W$ of $x_0$ in $X$ such that $W \times Y \subset N$. munkres topology solutions chapter 5
These exercises test your understanding of the universal property and the fact that $\beta X$ is the “maximum” compactification. $Y$ any space
A collection of sets has the FIP if every finite subcollection has a non-empty intersection. Munkres uses this to prove Tychonoff’s theorem by extending a collection with the FIP to a maximal collection. munkres topology solutions chapter 5