Some cardinal and topological properties of the $n$-permutation degree of a topological spaces and locally $\tau$-density of hyperspaces

In the paper we investigate some cardinal and topological properties of the $n$-permutation degree of a topological spaces and locally $\tau$-density of hyperspaces. It is proved that the functors $\exp_n$ and $SP^n$ preserves locally $\tau$-density of any infinite $T_1$-spaces.

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