KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 4

On localization of the star-Menger selection principle

Debraj Chandra
Nur Alam
Sayfa
1155–1168
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Besides, several results on decomposition and remainder of locally star-Menger spaces are also presented.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper we primarily introduce the local version of star-Menger property, namely locally star-Menger property (a space with this property is called locally star-Menger) and present some important topological observations.
📊
Temel Bulgular & Veri:Certain interactions between the new notion and star-Menger property are also observed.
💡
Sonuç & Katkı:Besides, several results on decomposition and remainder of locally star-Menger spaces are also presented.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:locally star-Menger · effectively locally star-Menger · Pixley-Roy hyperspace

Abstract

In this paper we primarily introduce the local version of star-Menger property, namely locally star-Menger property (a space with this property is called locally star-Menger) and present some important topological observations. Certain interactions between the new notion and star-Menger property are also observed. Some observations on effectively locally star-Menger Pixley-Roy hyperspaces (introduced here) are obtained. Preservation like properties under several topological operations are also interpreted carefully. Besides, several results on decomposition and remainder of locally star-Menger spaces are also presented.

🔖

Bu Makaleye Atıf Yap

Chandra, D., Alam, N. (2022). On localization of the star-Menger selection principle. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 4, 1155–1168. https://ajindex.com/articles/529470

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (21)

  1. A.V. Arhangel’skii, A class of spaces which contains all metric and all locally compact spaces, Mat. Sb. (N.S.), 67 (109), 55–88, 1965, English translation: Amer. Math. Soc. Transl. 92, 1–39, 1970
  2. A.V. Arhangel’skii, Mappings and spaces, Russian Math. Surveys, 21 (4), 115–162, 1966
  3. A.V. Arhangel’skii, Remainders in compactifications and generalized metrizability properties, Topology Appl. 150, 79–90, 2005
  4. A.V. Arhangel’skii, A generalization of Čech-complete spaces and Lindelöf $\Sigma$-spaces, Comment. Math. Univ. Carolin. 54 (2), 121–139, 2013
  5. A.V. Arhangel’skii, Remainders of metrizable and close to metrizable spaces, Fund. Math. 220, 71–81, 2013
  6. A.V. Arhangel’skii and M.M. Choban, Some generalizations of the concept of a $p$-space, Topology Appl. 158, 1381–1389, 2011
  7. A.S. Besicovitch, Concentrated and rarified sets of points, Acta Math. 62, 289–300, 1934
  8. M. Bonanzinga and M. Matveev, Some covering properties for $\Psi$-spaces, Mat. Vesnik, 61, 3–11, 2009
  9. J. Casas-de la Rose, S.A. Garcia-Balan and P.J. Szeptycki, Some star and strongly star selection principles, Topology Appl. 258, 572–587, 2019
  10. J. Cruz-Castillo, A. Ramírez-Páramo and J.F. Tenorio, Menger and Menger-type star selection principles for hit-and-miss topology, Topology Appl. 290, Art. ID 107574, 2021
  11. P. Daniels, Pixley-Roy spaces over subsets of the reals, Topology Appl. 29, 93–106, 1988
  12. R. Engelking, General Topology, Heldermann Verlag, Berlin, 1989
  13. L. Gillman and M. Jerison, Rings of Continuous Functions, Van Nostrand, Princeton, NJ, 1960
  14. K.P. Hart, J. Nagata and J.E. Vaughan, Encyclopedia of General Topology, Elsevier Science Publishers B. V., Amsterdam, 2004
  15. W. Hurewicz, Über eine Verallgemeinerung des Borelschen Theorems, Math. Z. 24, 401–421, 1926
  16. W. Just, A.W. Miller, M. Scheepers and P.J. Szeptycki, The combinatorics of open covers (II), Topology Appl. 73, 241–266, 1996
  17. Lj.D.R. Kočinac, Star-Menger and related spaces, Publ. Math. Debrecen, 55, 421–431, 1999
  18. Lj.D.R. Kočinac, The Pixley-Roy topology and selection principles, Questions Answers Gen. Topology, 19 (2), 219–225, 2001
  19. Lj.D.R. Kočinac, Star selection principles: A survey, Khayyam J. Math. 1 (1), 82– 106, 2015
  20. K. Menger, Einige Überdeckungssätze de Punktmengenlehre, Sitzungsber. Wien. Abt. 2a Math. Astronom. Phys. Meteorol. Mech. 133, 421–444, 1924
  21. E.A. Michael, Bi-quotient maps and cartesian products of quotien