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On the n -fold symmetric product of a space with a σ - ( P ) -property c n -network ( c k -network)

Luong Q. TuyenOng V. Tuyen — 2020

Commentationes Mathematicae Universitatis Carolinae

We study the relation between a space X satisfying certain generalized metric properties and its n -fold symmetric product n ( X ) satisfying the same properties. We prove that X has a σ - ( P ) -property c n -network if and only if so does n ( X ) . Moreover, if X is regular then X has a σ - ( P ) -property c k -network if and only if so does n ( X ) . By these results, we obtain that X is strict σ -space (strict -space) if and only if so is n ( X ) .

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