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Diffstat (limited to 'pages/general-topology/compactness/index.md')
| -rw-r--r-- | pages/general-topology/compactness/index.md | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/pages/general-topology/compactness/index.md b/pages/general-topology/compactness/index.md index 37e9b4d..6c2e274 100644 --- a/pages/general-topology/compactness/index.md +++ b/pages/general-topology/compactness/index.md @@ -26,7 +26,8 @@ if and only if it has the following property: then there exists a finite subcollection of $\mathcal{O}$ that covers $X$. If $\mathcal{A}$ is a collection of subsets of $X$, -let $\mathcal{A}^c = \braces{ X \setminus A : A \in \mathcal{A}}$ denote the collection of the complements of its members. +let $\mathcal{A}^c = \braces{ X \setminus A : A \in \mathcal{A}}$ denote +the collection of the complements of its members. Clearly, $\mathcal{B}$ is a subcollection of $\mathcal{A}$ if and only if $\mathcal{B}^c$ is a subcollection of $\mathcal{A}^c$. Moreover, note that $\mathcal{B}$ covers $X$ if and only if @@ -43,4 +44,3 @@ if and only if $\mathcal{A}^c$ consists of closed subsets of $X$. {% definition Finite Intersection Property%} TODO {% enddefinition %} - |