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Theorems · Theorem · commutative algebra

IsTopologicallyNilpotent.zero

∀ {R : Type u_1} [inst : TopologicalSpace R] [inst_1 : MonoidWithZero R], IsTopologicallyNilpotent 0

0 is topologically nilpotent

Defined in
Mathlib.Topology.Algebra.TopologicallyNilpotent
Cited by
1 results in Mathlib
Foundations
Depth 63 from the axioms · uses propext, Quot.sound
Assumes
TopologicalSpaceMonoidWithZero
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MvPowerSeries.HasEval.zero · cited by 3HasEval.zeroTopologicalSpace · cited by 24529TopologicalSpaceMonoidWithZero · cited by 456MonoidWithZerozero_pow · cited by 361zero_powIsTopologicallyNilpotent · cited by 22IsTopologicallyNilpotenttendsto_atTop_of_eventually_const · cited by 14tendsto_atTop_of_eventual…IsTopologicallyNilpotent.zeroCITED BYCITES

Cites5

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Cited by1

Results whose statement or proof uses this declaration.