Theorems · Theorem · functional analysis
ProperSpace.of_locallyCompactSpace
∀ (𝕜 : Type u_1) [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : SeminormedAddCommGroup E] [NormedSpace 𝕜 E]
[LocallyCompactSpace E], ProperSpace EA locally compact normed vector space is proper.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realproof · cited by 25,697
- NormedSpacestatement and proof · cited by 12,499
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Preorderproof · cited by 7,952
- Norm.normproof · cited by 5,413
- Filter.Tendstoproof · cited by 3,814
- SeminormedAddCommGroupstatement and proof · cited by 2,671
- Filter.atTopproof · cited by 2,405
- IsCompactproof · cited by 1,282
- Metric.closedBallproof · cited by 704
- smul_zeroproof · cited by 665
- Filter.Eventually.of_forallproof · cited by 526
Cited by6
Results whose statement or proof uses this declaration.
- FiniteDimensional.properproof · cited by 4
- stronglyMeasurable_deriv_with_paramproof · cited by 3
- measurableSet_of_differentiableAt_of_isComplete_with_paramproof · cited by 2
- MeasureTheory.ae_ae_add_linearMap_mem_iffproof · cited by 1
- ProperSpace.of_locallyCompact_moduleproof · cited by 1
- FDerivMeasurableAux.isOpen_A_with_paramproof · cited by 1