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Diffstat (limited to 'library/topology/urysohn2.tex')
| -rw-r--r-- | library/topology/urysohn2.tex | 14 |
1 files changed, 7 insertions, 7 deletions
diff --git a/library/topology/urysohn2.tex b/library/topology/urysohn2.tex index 838b121..83e3aa4 100644 --- a/library/topology/urysohn2.tex +++ b/library/topology/urysohn2.tex @@ -367,10 +367,10 @@ \end{subproof} Let $N = \seq{\zero}{k}$. Let $M = \pow{X}$. - Define $V : N \to M$ such that $V(n)=$ + Define $V : N \to M$ such that $V(n)= \begin{cases} - &\at{U}{F(n)} & \text{if} n \in N - \end{cases} + \at{U}{F(n)} & \text{if} n \in N + \end{cases}$ $\dom{V} = \seq{\zero}{k}$. We show that $V$ is a urysohnchain of $X$. \begin{subproof} @@ -445,11 +445,11 @@ $B \subseteq X'$ by \cref{powerset_elim,closeds}. $A \subseteq X'$. Therefore $A \subseteq A'$. - Define $U_0: N \to \{A, A'\}$ such that $U_0(n) =$ + Define $U_0: N \to \{A, A'\}$ such that $U_0(n) = \begin{cases} - &A &\text{if} n = \zero \\ - &A' &\text{if} n = 1 - \end{cases} + A &\text{if} n = \zero \\ + A' &\text{if} n = 1 + \end{cases}$ $U_0$ is a function. $\dom{U_0} = N$. $\dom{U_0} \subseteq \naturals$ by \cref{ran_converse}. |