Some Cardinal and Geometric Properties of the Space of Permutation Degree

Kočinac, Ljubiša D. R.; Mukhamadiev, Farkhod G.; Sadullaev, Anvar K.

doi:10.3390/axioms11060290

Open AccessEditor’s ChoiceArticle

Some Cardinal and Geometric Properties of the Space of Permutation Degree

by

Ljubiša D. R. Kočinac

^1,*

,

Farkhod G. Mukhamadiev

²

and

Anvar K. Sadullaev

³

¹

Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia

²

Department of Mathematics, National University of Uzbekistan named after Mirzo Ulugbek, Str. University 4, Tashkent 100174, Uzbekistan

³

Yeoju Technical Institute in Tashkent, Str. Usman Nasyr 156, Tashkent 100121, Uzbekistan

^*

Author to whom correspondence should be addressed.

Axioms 2022, 11(6), 290; https://doi.org/10.3390/axioms11060290

Submission received: 13 May 2022 / Revised: 9 June 2022 / Accepted: 13 June 2022 / Published: 14 June 2022

(This article belongs to the Special Issue Advances in General Topology and Its Application)

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Abstract

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

{SP}^{2} (R, τ (A))

of permutation degree of the Hattori space is discussed. In particular, it is shown that the space

{SP}^{2} (R, τ_{S})

contains a closed discrete subset of cardinality

c

. Moreover, it is shown that the functor

{SP}_{G}^{n}

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

{SP}_{G}^{n} X

and

{SP}_{G}^{n} Y

are also homotopically equivalent. As a result, it has been proved that the functor

{SP}_{G}^{n}

is a covariant homotopy functor.

Keywords: extent; Lindelöf number; hereditary cardinal invariant; homotopically equivalent; covariant homotopy functor; retract

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MDPI and ACS Style

Kočinac, L.D.R.; Mukhamadiev, F.G.; Sadullaev, A.K. Some Cardinal and Geometric Properties of the Space of Permutation Degree. Axioms 2022, 11, 290. https://doi.org/10.3390/axioms11060290

AMA Style

Kočinac LDR, Mukhamadiev FG, Sadullaev AK. Some Cardinal and Geometric Properties of the Space of Permutation Degree. Axioms. 2022; 11(6):290. https://doi.org/10.3390/axioms11060290

Chicago/Turabian Style

Kočinac, Ljubiša D. R., Farkhod G. Mukhamadiev, and Anvar K. Sadullaev. 2022. "Some Cardinal and Geometric Properties of the Space of Permutation Degree" Axioms 11, no. 6: 290. https://doi.org/10.3390/axioms11060290

APA Style

Kočinac, L. D. R., Mukhamadiev, F. G., & Sadullaev, A. K. (2022). Some Cardinal and Geometric Properties of the Space of Permutation Degree. Axioms, 11(6), 290. https://doi.org/10.3390/axioms11060290

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

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Some Cardinal and Geometric Properties of the Space of Permutation Degree

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