Category:Definitions/Lower Closures
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This category contains definitions related to Lower Closures.
Related results can be found in Category:Lower Closures.
Let $\struct {S, \preccurlyeq}$ be an ordered set.
Let $a \in S$.
The lower closure of $a$ (in $S$) is defined as:
- $a^\preccurlyeq := \set {b \in S: b \preccurlyeq a}$
That is, $a^\preccurlyeq$ is the set of all elements of $S$ that precede $a$.
Pages in category "Definitions/Lower Closures"
The following 21 pages are in this category, out of 21 total.
L
- Definition:Lower Closure
- Definition:Lower Closure of Element
- Definition:Lower Closure of Element (Class Theory)
- Definition:Lower Closure of Subset
- Definition:Lower Closure/Also defined as
- Definition:Lower Closure/Also known as
- Definition:Lower Closure/Element
- Definition:Lower Closure/Element/Also known as
- Definition:Lower Closure/Element/Class Theory
- Definition:Lower Closure/Set
S
- Definition:Strict Lower Closure
- Definition:Strict Lower Closure of Element
- Definition:Strict Lower Closure of Element (Class Theory)
- Definition:Strict Lower Closure of Subset
- Definition:Strict Lower Closure/Element
- Definition:Strict Lower Closure/Element/Also known as
- Definition:Strict Lower Closure/Element/Class Theory
- Definition:Strict Lower Closure/Set