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Theorems · Theorem · general topology

OnePoint.continuous_map

∀ {X : Type u_1} {Y : Type u_2} [inst : TopologicalSpace X] [inst_1 : TopologicalSpace Y] {f : X → Y},
  Continuous f → Filter.Tendsto f (Filter.coclosedCompact X) (Filter.coclosedCompact Y) → Continuous (OnePoint.map f)
Defined in
Mathlib.Topology.Compactification.OnePoint.Basic
Cited by
0 results in Mathlib
Foundations
Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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TopologicalSpace · cited by 24529TopologicalSpaceFilter.Tendsto · cited by 3814Filter.TendstoContinuous · cited by 2592ContinuousOnePoint · cited by 126OnePointFilter.coclosedCompact · cited by 20Filter.coclosedCompactOnePoint.map · cited by 12OnePoint.mapOnePoint.continuous_map_iff · cited by 1OnePoint.continuous_map_i…OnePoint.continuous_mapCITED BYCITES

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