Theorems · Theorem · general topology
Continuous.isOpen_support
∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [T1Space X] [inst_2 : Zero X] [inst_3 : TopologicalSpace Y]
{f : Y → X}, Continuous f → IsOpen (Function.support f)- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Continuousstatement and proof · cited by 2,592
- IsOpenstatement · cited by 2,400
- Function.supportstatement · cited by 610
- T1Spacestatement and proof · cited by 275
- IsOpen.preimageproof · cited by 147
- isOpen_neproof · cited by 22
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.addHaarScalarFactor_eq_mulproof · cited by 6
- MeasureTheory.Measure.haarScalarFactor_eq_mulproof · cited by 3
- IsOpen.exists_contDiff_support_eqproof · cited by 2
- eq_zero_or_locallyCompactSpace_of_support_subset_isCompact_of_addGroupproof · cited by 2
- eq_zero_or_locallyCompactSpace_of_support_subset_isCompact_of_groupproof · cited by 1
- MeasureTheory.integral_pos_of_integrable_nonneg_nonzeroproof · cited by 1