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## Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

#### Abstract

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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#### References

1. Fedorchuk V. V., Filippov V. V. Topology of hyperspaces and its applications. Topology and its Applications, 1989, V. 4, No. 4, pp.3–48.

2. Engelking R. General topology. Polish Scientific Publishers, 1986. – 626 p.

3. Beshimov R. B., Mukhamadiev F. G., Zhuraev R. M. Cardinal properties of the space of permutation degree. Scientific Reports of the Tashkent State Pedagogical University, 2014, No. 1(2), pp.76–84.

4. Beshimov R. B., Djabbarov G. F. On local weakly separable space. Methods Funct. Anal. Topology, 2005, V. 11, No. 3, pp.217–221.

5. Beshimov R. B., Mukhamadiev F. G. Some cardinal properties of complete linked systems with compact elements and absolute regular spaces. Mathematica Aeterna, 2013, V. 3, No. 8, pp.625–633.

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