Mathlib Map

Theorems · Definition · general topology

OnePoint.continuousMapMk

{X : Type u_1} →
  [inst : TopologicalSpace X] →
    {Y : Type u_3} →
      [inst_1 : TopologicalSpace Y] →
        (f : C(X, Y)) → (y : Y) → Filter.Tendsto (⇑f) (Filter.coclosedCompact X) (nhds y) → C(OnePoint X, Y)

A constructor for continuous maps out of a one point compactification, given a continuous map from the underlying space and a limit value at infinity.

Defined in
Mathlib.Topology.Compactification.OnePoint.Basic
Cited by
0 results in Mathlib
Foundations
Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
TopologicalSpaceTopologicalSpace
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Around this declaration

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

OnePoint.continuousMapMkDiscrete · cited by 0OnePoint.continuousMapMkD…DFunLike.coe · cited by 62936DFunLike.coeTopologicalSpace · cited by 24529TopologicalSpacenhds · cited by 5554nhdsFilter.Tendsto · cited by 3814Filter.TendstoContinuousMap · cited by 2491ContinuousMapOnePoint · cited by 126OnePointFilter.coclosedCompact · cited by 20Filter.coclosedCompactOnePoint.elim · cited by 3OnePoint.elimOnePoint.continuousMapMkCITED BYCITES

Cites8

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Cited by1

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