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Theorems · Theorem · general topology

isClopen_range_sigmaMk

∀ {ι : Type u_1} {X : ι → Type u_2} [inst : (i : ι) → TopologicalSpace (X i)] {i : ι}, IsClopen (Set.range (Sigma.mk i))
Defined in
Mathlib.Topology.Clopen
Cited by
1 results in Mathlib
Foundations
Depth 77 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.

Sigma.isConnected_iff · cited by 2Sigma.isConnected_iffTopologicalSpace · cited by 24529TopologicalSpaceSet.range · cited by 4705Set.rangeIsClopen · cited by 189IsClopenTopology.IsClosedEmbedding.isClosed_range · cited by 41IsClosedEmbedding.isClose…Topology.IsOpenEmbedding.isOpen_range · cited by 33IsOpenEmbedding.isOpen_ra…Topology.IsOpenEmbedding.sigmaMk · cited by 5IsOpenEmbedding.sigmaMkTopology.IsClosedEmbedding.sigmaMk · cited by 3IsClosedEmbedding.sigmaMkisClopen_range_sigmaMkCITED BYCITES

Cites7

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Cited by1

Results whose statement or proof uses this declaration.