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The locale corresponding to the real interval [ − 1, 1] is an interval object, in the sense of Escardó and Simpson, in the category of locales. The map    c  :   2  ω   →   [  −  1  ,  1  ]    , mapping a stream  s  of signs ±1 to∑   i  =  1   ∞    s  i    2   −  i, is a proper localic surjection; it is also expressed as a coequalizer. The proofs are valid in any elementary topos with natural numbers object.

The localic compact interval is an Escardó‐Simpson interval object