The Density and the Local Density of Space of the Permutation Degree and Hyperspaces

Mukhamadiev, F. G.; Badrutdinova, R. Z.; Sadullaev, Anvar K.; Meyliev, Sh. U.

doi:10.37418/amsj.10.1.29

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2022

2024

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“…In the investigations in [11,12], the concept of symmetric product of a topological space is introduced. In particular, in [13] the functor SP n G is studied, and some cardinal and topological properties of this functor were investigated. In [14], some propositions about homotopy properties of the topological spaces were proved.…”

Section: Introductionmentioning

confidence: 99%

Some Cardinal and Geometric Properties of the Space of Permutation Degree

Kočinac

Mukhamadiev

Sadullaev

2022

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This paper is devoted to the investigation of cardinal invariants such as the hereditary density, hereditary weak density, and hereditary Lindelöf number. The relation between the spread and the extent of the space SP2(R,τ(A)) of permutation degree of the Hattori space is discussed. In particular, it is shown that the space SP2(R,τS) contains a closed discrete subset of cardinality c. Moreover, it is shown that the functor SPGn preserves the homotopy and the retraction of topological spaces. In addition, we prove that if the spaces X and Y are homotopically equivalent, then the spaces SPGnX and SPGnY are also homotopically equivalent. As a result, it has been proved that the functor SPGn is a covariant homotopy functor.

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Section: Introductionmentioning

confidence: 99%