Theorems · Theorem · general topology
Continuous.bddBelow_range_of_hasCompactSupport
∀ {α : Type u_2} {β : Type u_3} [inst : LinearOrder α] [inst_1 : TopologicalSpace α] [inst_2 : TopologicalSpace β]
[ClosedIicTopology α] [inst_4 : Zero α] {f : β → α}, Continuous f → HasCompactSupport f → BddBelow (Set.range f)A continuous function with compact support is bounded below.
- Defined in
- Mathlib.Topology.Order.Compact
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement and proof · cited by 24,529
- LinearOrderstatement and proof · cited by 8,572
- Set.rangestatement · cited by 4,705
- Continuousstatement and proof · cited by 2,592
- BddBelowstatement · cited by 401
- HasCompactSupportstatement and proof · cited by 196
- ClosedIicTopologystatement and proof · cited by 115
- IsCompact.bddBelowproof · cited by 8
- HasCompactSupport.isCompact_rangeproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Continuous.bddAbove_range_of_hasCompactSupportproof · cited by 3