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Compact subsets of free algebras with topologies and equivalence of spaces. (English) Zbl 1138.54312

Summary: We investigate universal algebras with topologies. On algebras we consider topologies relatively to which operations are continuous on compact subsets. These algebras are called \(k\)-algebras. Some properties of compact subsets of free \(k\)-algebras and some facts about \(M_V\)-equivalence of spaces are established.

MSC:

54H13 Topological fields, rings, etc. (topological aspects)
54A25 Cardinality properties (cardinal functions and inequalities, discrete subsets)
08B20 Free algebras
54C40 Algebraic properties of function spaces in general topology
54D30 Compactness
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