## American Mathematical Society TranslationsTranslations of articles on mathematics appearing in various Russian mathematical serials. |

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### Contents

Melnichuk HausdorfF dimension in Diophantine approximations | 1 |

AlteeHiiiTaT h B K BoryTa 0 peuieTKe MHoroo6pa3Hft nojiyrpynn | 3 |

B n CojiTaH HeKOTopwe CBoftcTBa dBbinyKjibix cbyHKUHH H H3bccthh | 21 |

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### Common terms and phrases

7r-base Akad Algebra Amer arbitrary Assertion atoms axiom balanced identities base of identities boundary correspondence caliber cardinality closure commutative semigroups compact Hausdorff space compact space compactification Consequently consider construct contains continuum convergence convex COROLLARY countable tightness d-conv d-convex function d-face d-separation defined denote Dokl domains E. S. Lyapin editor English transl equation example exists follows free semigroups hence hereditarily finitely based homeomorphism idempotent idempotent semigroups inequality Inst isomorphic Lemma Leningrad Martin's axiom Mathematics Subject Classification metric space n-base Nauk SSSR Noetherian nonempty normal obtained open subsets Ovchinnikov permutational identity prime ends problem Proc PROOF properties proved regular cardinal relative metric result Russian satisfying Semigroup Forum semigroup varieties sequence solvability Soviet Math subfamily sublattice subvarieties Suppose Suslin condition Suvorov system of identities Theorem 2.1 Theory of Semigroups topological spaces topology Univ varieties of semigroups vector weakly Noetherian