Algebras of multiplace functions

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Designations Introduction 1 Main concepts1.1 Elements of the theory of relations1.2 Functions and operations1.3 Algebraic systems1.4 Closure operations1.5 Notes on Chapter 1 2 Menger algebras of functions2.1 Definitions and fundamental notions2.2 Menger semigroups2.3 v-regular Menger algebras2.4 i-solvable Menger algebras2.5 Group-like Menger algebras2.6 Antisymmetric Menger algebras2.7 Representations of Menger algebras2.8 Notes on Chapter 2 3 Ordered Menger algebras3.1 Menger algebras of relations3.2 F.o. and p.q-o. Menger algebras3.3 Algebras of reversive functions3.4 (f)-, (g)-, (f,g)-Menger algebras3.5 Subtraction Menger algebras3.6 Restrictive Menger algebras3.7 Functional Menger systems3.8 Notes on Chapter 3 4 Relations between functions4.1 Stabilizers of Menger algebras4.2 Stabilizers of functional Menger systems4.3 Stationary subsets4.4 Semi-compatibility relation4.5 Co-definability relation4.6 Connectivity relation4.7 Projection equivalence relation4.8 Semiadjacency relation4.9 Notes on Chapter 4 5 (2, n)-semigroups of functions5.1 (2, n)-semigroups and their representations5.2 Menger (2, n)-semigroups5.3 Projection relations on (2, n)-semigroups5.4 Notes on Chapter 5 6 Systems of multiplace functions6.1 Menger systems6.2 Menger T-systems6.3 Positional algebras6.4 Mal'cev-Post iterative algebras6.5 Semigroups of functions6.6 Central semigroups of operations6.7 Algebras of vector-valued functions6.8 Notes on Chapter 6 7 Open problems7.1 Closure operations7.2 Menger algebras of functions7.3 Menger algebras of relations7.4 (2, n)-semigroups7.5 Positional algebras Bibliography Index