Mathlib Map

Theorems · Theorem · general topology

ContinuousMap.ext

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f g : C(X, Y)},
  (∀ (a : X), f a = g a) → f = g
Defined in
Mathlib.Topology.ContinuousMap.Defs
Cited by
92 results in Mathlib
Foundations
Depth 14 from the axioms · uses Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

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

CFC.exp_eq_normedSpace_exp · cited by 5CFC.exp_eq_normedSpace_expContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints · cited by 4ContinuousMap.starSubalge…ContinuousMapZero.mkD_eq_mkD_of_map_zero · cited by 4ContinuousMapZero.mkD_eq_…LightProfinite.epi_iff_surjective · cited by 3LightProfinite.epi_iff_su…ContinuousMap.comp_const · cited by 3ContinuousMap.comp_constCompHausLike.pullback.condition · cited by 3pullback.conditionCompHaus.effectiveEpiFamily_tfae · cited by 3CompHaus.effectiveEpiFami…IsQuotientCoveringMap.monodromy_toPermFiber · cited by 3IsQuotientCoveringMap.mon…ContinuousMap.Homotopy.curry_one · cited by 2Homotopy.curry_oneContinuousMap.Homotopy.curry_zero · cited by 2Homotopy.curry_zeroSubalgebra.SeparatesPoints.rclike_to_real · cited by 2SeparatesPoints.rclike_to…cfc_integral' · cited by 2cfc_integral'gelfandTransform_map_star · cited by 2gelfandTransform_map_starContinuousMap.summable_of_locally_summable_norm · cited by 2ContinuousMap.summable_of…ContinuousMap.comp_id · cited by 2ContinuousMap.comp_idDFunLike.coe · cited by 62936DFunLike.coeTopologicalSpace · cited by 24529TopologicalSpaceContinuousMap · cited by 2491ContinuousMapDFunLike.ext · cited by 240DFunLike.extContinuousMap.extCITED BYCITES

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Cited by92

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