Structures · Topology
ContinuousSup
Let L be a topological space and let L×L be equipped with the product topology and let
⊓:L×L → L be a supremum. Then L is said to have (jointly) continuous supremum if the map
⊓:L×L → L is continuous.
- Defined in
- Mathlib.Topology.Order.Lattice
- Shape
- One type argument · adds continuous_sup
Extends0
Extends nothing: this is a root of the hierarchy.
Extended by1
Concrete types that are instances4
- TopologicalSpace.NonemptyCompacts
- TopologicalSpace.Compacts
- TopologicalSpace.Closeds
- OrderDual
How is a type an instance?
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Assumed by78
- MeasureTheory.StronglyMeasurable.sup
- MeasureTheory.AEStronglyMeasurable.sup
- MeasureTheory.AEEqFun.coeFn_sup
- Filter.Tendsto.finset_sup'_nhds
- Filter.Tendsto.sup_nhds
- Filter.Tendsto.finset_sup_nhds_apply
- Filter.Tendsto.finset_sup'_nhds_apply
- Filter.Tendsto.sup_nhds'
- ContinuousAt.finset_sup_apply
- ContinuousWithinAt.finset_sup_apply
- Filter.Tendsto.partialSups_apply
- ContinuousWithinAt.finset_sup'_apply
- MeasureTheory.Submartingale.pos
- ContinuousAt.sup'
- ContinuousWithinAt.sup'
- Continuous.sup
- ContinuousAt.finset_sup'_apply
- ContinuousAt.partialSups_apply
- ContinuousWithinAt.partialSups_apply
- Filter.Tendsto.finset_sup_nhds
- continuous_sup
- ContinuousWithinAt.finset_sup'
- ContinuousMap.sup'_apply
- CompactlySupportedContinuousMap.finsetSup'_apply
- Filter.Tendsto.partialSups
- ContinuousAt.finset_sup
- ContinuousAt.partialSups
- ContinuousWithinAt.partialSups
- MeasureTheory.FinStronglyMeasurable.sup
- ContinuousOn.sup'
- MeasureTheory.AEStronglyMeasurable.fun_sup
- ContinuousOn.sup
- MeasureTheory.Submartingale.sup
- Continuous.finset_sup
- ContinuousMap.coe_sup'
- ContinuousAt.finset_sup'
- ContinuousWithinAt.finset_sup
- ContinuousSup.continuous_sup
- ContinuousMap.sup_apply
- MeasureTheory.StronglyMeasurable.fun_sup
- MeasureTheory.AEStronglyMeasurable.posPart
- CompactlySupportedContinuousMap.sup_apply
- MeasureTheory.AEEqFun.le_sup_left
- Continuous.finset_sup'_apply
- ContinuousOn.finset_sup
- ContinuousOn.partialSups_apply
- ContinuousMap.semilatticeSup
- ContinuousOn.partialSups
- MeasureTheory.StronglyMeasurable.oneLePart
- ContinuousAt.sup
Ancestors0
No ancestors.