diff options
Diffstat (limited to 'library')
| -rw-r--r-- | library/topology/topological-space.tex | 6 |
1 files changed, 5 insertions, 1 deletions
diff --git a/library/topology/topological-space.tex b/library/topology/topological-space.tex index 2590287..dd236bb 100644 --- a/library/topology/topological-space.tex +++ b/library/topology/topological-space.tex @@ -233,7 +233,11 @@ \end{proposition} \begin{proof} \begin{byCase} - \caseOf{$F$ is empty.} Trivial. + \caseOf{$F$ is empty.} + For all $X$ we have $X \notin F$. + If $X \in F$ and $A \in X$ then $A \in F$. + %There exist $X \in F$. + Contradiction by assumption. \caseOf{$F$ is inhabited.} There exist $X \in F$ such that $X \subseteq \unions{F}$. $A \subseteq X \subseteq \unions{F}$. |