Theorems · Theorem · general topology
HasCompactMulSupport.isCompact_preimage
∀ {α : Type u_2} {β : Type u_4} [inst : TopologicalSpace α] [inst_1 : One β] {f : α → β} [inst_2 : TopologicalSpace β]
{K : Set β}, HasCompactMulSupport f → Continuous f → IsClosed K → 1 ∉ K → IsCompact (f ⁻¹' K)- Defined in
- Mathlib.Topology.Algebra.Support
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- 0 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- Set.preimagestatement and proof · cited by 4,946
- Continuousstatement and proof · cited by 2,592
- IsClosedstatement and proof · cited by 1,639
- IsCompactstatement · cited by 1,282
- IsClosed.preimageproof · cited by 138
- IsCompact.of_isClosed_subsetproof · cited by 67
- HasCompactMulSupportstatement and proof · cited by 43
- subset_mulTSupportproof · cited by 6
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