Added extremely disconnected spaces.
All checks were successful
Compile Project / Compile (push) Successful in 40s
All checks were successful
Compile Project / Compile (push) Successful in 40s
This commit is contained in:
@@ -60,7 +60,7 @@
|
||||
|
||||
is open. On the other hand, let $x \in X$, then $f(x) > \alpha$ if and only if there exists $q \in (\alpha, f(x)) \cap \rational$ such that $x \not\in U_q$. By (b) of (1), this is equivalent to the existence of $p \in (\alpha, f(x)) \cap \rational$ such that $x \not\in \ol{U_p}$. In which case,
|
||||
\[
|
||||
f^{-1}((b, 1]) = \bigcup_{\substack{q \in \rational \cap [0, 1] \\ q > \alpha}}\overline{U_p}^c
|
||||
f^{-1}((\alpha, 1]) = \bigcup_{\substack{q \in \rational \cap [0, 1] \\ q > \alpha}}\overline{U_p}^c
|
||||
\]
|
||||
|
||||
is open.
|
||||
|
||||
Reference in New Issue
Block a user