Universal nowhere dense and meager sets in Menger manifolds

In each Menger manifold M we construct:• ed nowhere dense subset M 0 which is homeomorphic to M and is universal nowhere dense in the sense that for each nowhere dense set A ⊂ M there is a homeomorphism h of M such that h ( A ) ⊂ M 0 ; er F σ -set Σ 0 ⊂ M which is universal meager in the sense that for each meager subset B ⊂ M there is a homeomorphism h of M such that h ( B ) ⊂ Σ 0 . we prove that any two universal meager F σ -sets in M are ambiently homeomorphic.