Theorems · Theorem · functional analysis
ContinuousLinearMap.IsIdempotentElem.isClosed_range
∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : TopologicalSpace M] [inst_2 : AddCommGroup M]
[inst_3 : Module R M] [IsTopologicalAddGroup M] [T1Space M] {p : M →L[R] M}, IsIdempotentElem p → IsClosed ↑(↑p).range- Cited by
- 0 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
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
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupstatement and proof · cited by 12,871
- SetLike.coestatement · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- ContinuousLinearMapstatement and proof · cited by 5,352
- IsClosedstatement · cited by 1,639
- IsTopologicalAddGroupstatement and proof · cited by 1,394
- LinearMap.rangestatement · cited by 893
- ContinuousLinearMap.toLinearMapstatement · cited by 528
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