diff options
Diffstat (limited to 'library/topology')
| -rw-r--r-- | library/topology/real-topological-space.tex | 14 |
1 files changed, 11 insertions, 3 deletions
diff --git a/library/topology/real-topological-space.tex b/library/topology/real-topological-space.tex index 8757ffb..1c5e4cb 100644 --- a/library/topology/real-topological-space.tex +++ b/library/topology/real-topological-space.tex @@ -132,9 +132,17 @@ \begin{proof} $x - \epsilon \in \reals$. $x + \epsilon \in \reals$. - - It suffices to show that for all $c$ such that $c \in \reals \land (x - \epsilon) < c < (x + \epsilon)$ we have $c \in \epsBall{x}{\epsilon}$. - %Fix $c$ such that $c \in \reals \land (x - \epsilon) < c < (x + \epsilon)$. + + + %It suffices to show that for all $c$ such that $c \rless x$ we have $c \in \epsBall{x}{\epsilon}$. + %Fix $c$ such that $c \rless x$. +% + %It suffices to show that for all $c$ such that $c < x$ we have $c \in \epsBall{x}{\epsilon}$. + %Fix $c$ such that $c < x$. + + + It suffices to show that for all $c$ such that $c \in \reals \land (x - \epsilon) \rless c \rless (x + \epsilon)$ we have $c \in \epsBall{x}{\epsilon}$. + Fix $c$ such that $(c \in \reals) \land (x - \epsilon) \rless c \rless (x + \epsilon)$. %Suppose $(x - \epsilon) < c < (x + \epsilon)$. \end{proof} |