Theorems · Theorem · general topology
isClosedMap_const
∀ {X : Type u_3} {Y : Type u_4} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] [T1Space Y] {y : Y},
IsClosedMap (Function.const X y)- Defined in
- Mathlib.Topology.Separation.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 68 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.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.Nonemptyproof · cited by 2,627
- IsClosedproof · cited by 1,639
- Set.image_congrproof · cited by 533
- T1Spacestatement and proof · cited by 275
- IsClosedMapstatement · cited by 138
- Set.Nonempty.image_constproof · cited by 26
- IsClosedMap.of_nonemptyproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- isClosedMap_smul₀proof · cited by 2
- Polynomial.isClosedMap_evalproof · cited by 2
- isProperMap_const_iffproof · cited by 1
- isClosedMap_smul_leftproof · cited by 0