This commit is contained in:
parent
bbb891594c
commit
a0cc70cadf
2
.gitmodules
vendored
2
.gitmodules
vendored
@ -1,3 +1,3 @@
|
||||
[submodule "LatexPackagesBuild"]
|
||||
path = LatexPackagesBuild
|
||||
url = https://gitlab.com/latexci/packages/LatexPackagesBuild.git
|
||||
url = https://git.abstractnonsen.se/latex/latex-packages-build
|
||||
|
@ -160,14 +160,14 @@ Let $I$ be a linear order
|
||||
we have that $F_\gamma = \bigcap_{\alpha < \gamma} F_\alpha$,
|
||||
since $(X_\gamma,\Z)$ is the inverse limit of
|
||||
$\{(X_{\alpha}, \Z):\alpha < \gamma\}$.
|
||||
\item For all $\alpha < \beta$, $F_{\alpha+1} \subsetneq F_\alpha$,
|
||||
\item For all $\alpha$ it is $F_{\alpha+1} \subsetneq F_\alpha$,
|
||||
because $\pi^{\alpha+1}_\alpha \colon (X_{\alpha+1},\Z) \to (X_\alpha,\Z)$
|
||||
is not a bijection
|
||||
and all the fibers are isomorphic.
|
||||
\end{itemize}
|
||||
|
||||
So $(F_\alpha)_{\alpha \le \beta}$ is a strictly
|
||||
increasing chain of closed subsets.
|
||||
decreasing chain of closed subsets.
|
||||
But $X$ is second countable,
|
||||
so $\beta$ is countable:
|
||||
Let $\{U_n\} = \cB$ be a countable basis
|
||||
|
Loading…
Reference in New Issue
Block a user