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Theorems · Theorem · general topology

Filter.Tendsto.isCompact_insert_range

∀ {X : Type u} [inst : TopologicalSpace X] {f : ℕ → X} {x : X},
  Filter.Tendsto f Filter.atTop (nhds x) → IsCompact (insert x (Set.range f))
Defined in
Mathlib.Topology.Compactness.Compact
Cited by
1 results in Mathlib
Foundations
Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpace
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Around this declaration

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

Rat.not_countably_generated_cocompact · cited by 1Rat.not_countably_generat…Set · cited by 53352SetTopologicalSpace · cited by 24529TopologicalSpacenhds · cited by 5554nhdsSet.range · cited by 4705Set.rangeFilter.Tendsto · cited by 3814Filter.TendstoFilter.atTop · cited by 2405Filter.atTopIsCompact · cited by 1282IsCompactNat.cofinite_eq_atTop · cited by 37Nat.cofinite_eq_atTopFilter.Tendsto.isCompact_insert_range_of_cofinite · cited by 1Tendsto.isCompact_insert_…Tendsto.isCompact_insert_rangeCITED BYCITES

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Cited by1

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