Category:Limits Inferior of Nets
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This category contains results about Limits Inferior of Nets.
Definitions specific to this category can be found in Definitions/Limits Inferior of Nets.
Let $\struct {S, \preceq}$ be a directed set.
Let $L = \struct {T, \precsim}$ be a complete lattice.
Let $N: S \to T$ be a net in $T$.
Then limit inferior of $N$ is defined as follows:
- $\liminf N := \sup_L \set { {\map {\inf_L} {N \sqbrk {\map \preceq j} } : j \in S} }$
where
Pages in category "Limits Inferior of Nets"
The following 7 pages are in this category, out of 7 total.
L
M
- Mapping at Limit Inferior Precedes Limit Inferior of Composition Mapping and Sequence implies Mapping is Increasing
- Mapping at Limit Inferior Precedes Limit Inferior of Composition Mapping and Sequence implies Mapping Preserves Directed Suprema
- Mapping at Limit Inferior Precedes Limit Inferior of Composition Mapping and Sequence implies Supremum of Image is Mapping at Supremum of Directed Subset