IJAM: Volume 38, No. 3 (2025)

DOI: 10.12732/ijam.v38i3.5

ON ISOLATED POINTS OF THE
THIN SUPERKERNEL OF
COMPACT SPACES

 

Farkhod G. Mukhamadiev 1,2,ยง, Shakhboz U. Meyliev 1

 

1 National University of Uzbekistan
Tashkent - 100174, UZBEKISTAN
2 Kimyo International University in Tashkent
Tashkent - 100121, UZBEKISTAN

 

Abstract. In this work, we study some properties of the set of isolated points of the thin superkernel of compact spaces. We prove that for a T1-space, we have that $I (\lambda X) \subset \lambda* X$, i.e. each isolated point in \lambda X must be a thin maximal linked system. Also prove that for an infinite compact space X with $I(X)=\emptyset$, then $I (\lambda X) =\emptyset$, i.e. if X is a pointless space, then its superextension \lambda X is also pointless.

 

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How to cite this paper?
DOI: 10.12732/ijam.v38i3.5
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2025
Volume: 38
Issue: 3

References

[1] Lj.D.R. Kocinac, F.G. Mukhamadiev, Some properties of the N-nucleus, Topology and its Applications, 326 (2023), Art. 108430.

[2] Lj.D.R. Kocinac, F.G. Mukhamadiev, A.K. Sadullaev, Tightness type properties of the space of permutation degree. Mathematics, 10, No 18 (2022), Art. 3341, 1-7.

[3] Lj.D.R. Kocinac, F.G. Mukhamadiev, A.K. Sadullaev, and M.I. Akhmedov, On the superextension functor, AIP Conference Proceedings, 2879, No 1 (2023), Art. 020004.

[4] F.G. Mukhamadiev, On certain cardinal properties of the N-Nucleus of a space X, Journal of Mathematical Sciences, 245, No 3 (2020), 411-415.

[5] F.G. Mukhamadiev, Some topological and cardinal properties of the N--nucleus of a space X, Applied General Topology, 24, No 2 (2023), 423-432.

[6] F.G. Mukhamadiev, R.M. Zhuraev, On uniform structures in the space of n - permutation degree, International Journal of Applied Mathematics, 37, No 5 (2024), 539-543; DOI:10.12732/ijam.v37i5.5.

[7] T.K. Yuldashev, F.G. Mukhamadiev, Caliber of space of subtle complete coupled systems, Lobachevskii Journal of Mathematics, 42, No 12 (2021), 3043-3047.

[8] T.K. Yuldashev, F.G. Mukhamadiev, Some topological and cardinal properties of the \lambda-nucleus of a topological space X, Lobachevskii Journal of Mathematics, 44, No 4 (2023), 1513-1517

 

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