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Commit 2020-02-08 13:25 bcb63ebf

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refactor(topology/*): irreducible and connected sets are nonempty (#1964)

  • refactor(topology/*): irreducible and connected sets are nonempty
  • Fix typos
  • Fix more typos
  • Update src/topology/subset_properties.lean Co-Authored-By: sgouezel sebastien.gouezel@univ-rennes1.fr
  • Update src/topology/subset_properties.lean Co-Authored-By: sgouezel sebastien.gouezel@univ-rennes1.fr
  • Refactor 'nonempty' fields
  • Fix spacing in set-builder
  • Use dot notation
  • Write a comment on the nonempty assumption
  • Apply suggestions from code review
  • Fix build
  • Tiny improvements

Estimated changes

modified theorem intermediate_value_univ
modified theorem is_connected_Icc
deleted theorem is_connected_Ici
deleted theorem is_connected_Ico
deleted theorem is_connected_Iic
deleted theorem is_connected_Iio
deleted theorem is_connected_Ioc
deleted theorem is_connected_Ioi
modified theorem is_connected_Ioo
added theorem is_preconnected_Ici
added theorem is_preconnected_Ico
added theorem is_preconnected_Iic
added theorem is_preconnected_Iio
added theorem is_preconnected_Ioc
added theorem is_preconnected_Ioi
deleted theorem exists_irreducible
deleted theorem exists_mem_inter
added theorem exists_preirreducible
modified theorem is_clopen_iff
added theorem is_connected.nonempty
modified theorem is_connected.union
deleted theorem is_connected_closed_iff
deleted theorem is_connected_empty
deleted theorem is_connected_of_forall
deleted theorem is_connected_sUnion
added theorem is_irreducible.closure
added theorem is_irreducible.image
deleted theorem is_irreducible_closure
deleted theorem is_irreducible_empty
added theorem is_preconnected.image
added theorem is_preconnected.union
added def is_preconnected
added theorem is_preconnected_empty
added theorem is_preconnected_sUnion
added theorem nonempty_inter
modified theorem subset_connected_component