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    Which outer reloids are equal to inner ones
Warning: This formulation is vague (not exact).
Question   Characterize the set  . In other words, simplify this formula.
. In other words, simplify this formula. 
 . In other words, simplify this formula.
. In other words, simplify this formula. The problem seems rather difficult.
See Algebraic General Topology for definitions of used concepts.
Bibliography
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