Category:Upper Closures
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This category contains results about Upper Closures in the context of Order Theory.
Definitions specific to this category can be found in Definitions/Upper Closures.
Let $\struct {S, \preccurlyeq}$ be an ordered set.
Let $a \in S$.
The upper closure of $a$ (in $S$) is defined as:
- $a^\succcurlyeq := \set {b \in S: a \preccurlyeq b}$
That is, $a^\succcurlyeq$ is the set of all elements of $S$ that succeed $a$.
Pages in category "Upper Closures"
The following 26 pages are in this category, out of 26 total.
I
- Infimum of Image of Upper Closure of Element under Increasing Mapping
- Infimum of Intersection of Upper Closures equals Join Operands
- Infimum of Upper Closure of Element
- Infimum of Upper Closure of Set
- Intersection of Upper Closures is Upper Closure of Join Operands
- Inverse Image under Order Embedding of Strict Upper Closure of Image of Point
S
U
- Upper and Lower Closures are Convex
- Upper Closure in Ordered Subset is Intersection of Subset and Upper Closure
- Upper Closure is Closure Operator
- Upper Closure is Decreasing
- Upper Closure is Smallest Containing Upper Section
- Upper Closure is Strict Upper Closure of Immediate Predecessor
- Upper Closure is Upper Section
- Upper Closure of Coarser Subset is Subset of Upper Closure
- Upper Closure of Element is Filter
- Upper Closure of Singleton
- Upper Closure of Subset is Subset of Upper Closure