Theorems · Theorem · general topology

isSigmaCompact_range

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  Continuous f → ∀ [SigmaCompactSpace X], IsSigmaCompact (Set.range f)

If X is σ-compact, im f is σ-compact.

Defined in: Mathlib.Topology.Compactness.SigmaCompact
Cited by: 0 results in Mathlib
Foundations: Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: TopologicalSpace TopologicalSpace SigmaCompactSpace

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TopologicalSpacestatement and proof · cited by 24,529
Set.rangestatement · cited by 4,705
Continuousstatement and proof · cited by 2,592
Set.image_univproof · cited by 322
SigmaCompactSpacestatement and proof · cited by 55
IsSigmaCompactstatement · cited by 24
IsSigmaCompact.imageproof · cited by 2
isSigmaCompact_univproof · cited by 1

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