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We assume that S is a locally connected, connected, compact metric space and that P is a property of point sets. For any two points a and b of S we denote by C(ab) (respectively d(ab)) a closed (closed irreducible) cutting of S between the points a and b. We consider the following properties:doi:10.1090/s0002-9904-1939-06964-4 fatcat:qno4uwfhbjfa3ckkioc5fnxrri