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Theorems · Theorem · general topology

eq_of_germ_isConstant

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] {f : X → Y} [i : PreconnectedSpace X],
  (∀ (x : X), (↑f).IsConstant) → ∀ (x x' : X), f x = f x'
Defined in
Mathlib.Topology.Germ
Cited by
1 results in Mathlib
Foundations
Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpacePreconnectedSpace
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Around this declaration

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

eq_of_germ_isConstant_on · cited by 0eq_of_germ_isConstant_onTopologicalSpace · cited by 24529TopologicalSpacenhds · cited by 5554nhdsFilter.Germ.ofFun · cited by 73Germ.ofFunPreconnectedSpace · cited by 64PreconnectedSpaceFilter.Germ.IsConstant · cited by 9Germ.IsConstantIsLocallyConstant.apply_eq_of_isPreconnected · cited by 5IsLocallyConstant.apply_e…preconnectedSpace_iff_univ · cited by 2preconnectedSpace_iff_univIsLocallyConstant.of_germ_isConstant · cited by 1IsLocallyConstant.of_germ…eq_of_germ_isConstantCITED BYCITES

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Cited by1

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