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Some properties generalizing the normality separation axiom and their behavior under basic topological operations and continuous mappings are discussed. One of the general problems considered in the paper concerns the deduction of “nice” topological properties of spaces from generalized normality of certain topological products, their subspaces, and other related structures; in particular, extensions of the well-known theorems of Katetov and Tamano are suggested.

Some Normality-Type Properties, Topological Products, and Classes of Continuous Mappings