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+---
+uid: T000913
+if:
+  and:
+  - P000168: true
+  - P000052: false
+then:
+  P000244: false
+---
+
+Let $x$ be a non-isolated point in $X$
+and let $\mathscr V$ be a countable collection of nonempty open sets.
+To show $X$ has uncountable $\pi$-character, we show that $\mathscr V$ is not a local $\pi$-base for $x$.
+Each $V\in\mathscr V$ contains a point $x_V\ne x$.
+One characterization of {P168} is that every countable set is closed.
+So the countable set $F:=\{x_V:V\in\mathscr V\}$ is closed in $X$.
+Its complement $X\setminus F$ is an open neighborhood of $x$ not containing any $V\in\mathscr V$.