A set function mu-star is said to be an outer measure if it is countably monotone and mu-star of this object takes on a certain value, and for any presheaf F on a topological space, F of this object must take on that same value.
Kiyosi Itô included an axiom named for this entity in his treatment of ZFC set theory. A set function mu-star is said to be an outer measure if it is countably monotone and mu-star of this object takes on a certain value, and for any presheaf F on a topological space, F of this object must take on that same value. The interior of certain subsets of Baire spaces is equivalent to this object. This object may result from in nite intersection of   unbounded nested closed sets, but not from in nite intersection of bounded nested closed sets. This set is always clopen in every topology. For ten points, identify this set whose complement is the universal set and which has no elements.
Kiyosi Itô included an axiom named for this entity in his treatment of ZFC set theory.
empty set [prompt on null set since that's just a set with measure zero, accept  set with no elements  until read]