6
$\begingroup$

How do we show the following?

Let $X$ be a topological space and let $x \in X$. Show that if $x$ has a countable neighborhood basis in $X$ then $x$ has a countable neighborhood basis in $\beta X$. Here $\beta X$ denotes the Stone–Čech compactification of $X$.

  • 1
    One thinks about what the topology on $\beta X$ is.2010-12-01
  • 0
    @Arturo: The Tychonoff product topology. Then what to do?2010-12-01

1 Answers 1