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Theorems · Theorem · general topology

IsCompact.preimage_of_isOpen

∀ {α : Type u_2} {β : Type u_3} [inst : TopologicalSpace α] [inst_1 : TopologicalSpace β] {f : α → β} {s : Set β},
  IsSpectralMap f → IsCompact s → IsOpen s → IsCompact (f ⁻¹' s)
Defined in
Mathlib.Topology.Spectral.Hom
Cited by
2 results in Mathlib
Foundations
Depth 51 from the axioms · uses propext, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsCompactOpenCovered.of_finite_of_isSpectralMap · cited by 0IsCompactOpenCovered.of_f…IsSpectralMap.comp · cited by 0IsSpectralMap.compSet · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpaceSet.preimage · cited by 4946Set.preimageIsOpen · cited by 2400IsOpenIsCompact · cited by 1282IsCompactIsSpectralMap · cited by 20IsSpectralMapIsSpectralMap.isCompact_preimage_of_isOpen · cited by 5IsSpectralMap.isCompact_p…IsCompact.preimage_of_isOpenCITED BYCITES

Cites7

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Cited by2

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