Category:Separated Sets
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This category contains results about Separated Sets in the context of Topology.
Let $T = \struct {S, \tau}$ be a topological space.
Let $A, B \subseteq S$.
Definition 1
$A$ and $B$ are separated (in $T$) if and only if:
- $A^- \cap B = A \cap B^- = \O$
where:
Definition 2
$A$ and $B$ are separated (in $T$) if and only if there exist $U,V\in\tau$ with:
- $A \subset U$ and $U \cap B = \O$
- $B \subset V$ and $V \cap A = \O$
where $\O$ denotes the empty set.
$A$ and $B$ are said to be separated sets (of $T$).
Subcategories
This category has only the following subcategory.
Pages in category "Separated Sets"
The following 8 pages are in this category, out of 8 total.