Almost strongly star-Menger and related properties

• Cruz-Castillo, Ricardo ^[1] ; Ramírez-Páramo, Alejandro ^[2] ; Tenorio, Jesús F. ^[3]
  1. [1] Universidad Autónoma del Estado de Hidalgo

     Universidad Autónoma del Estado de Hidalgo

     México

     
  2. [2] Benemérita Universidad Autónoma de Puebla

     Benemérita Universidad Autónoma de Puebla

     México

     
  3. [3] Universidad Tecnológica de la Mixteca

     Universidad Tecnológica de la Mixteca

     México

     

  Mostrar afiliaciones +
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 26, Nº. 2, 2025, págs. 641-656
• Idioma: inglés
• DOI: 10.4995/agt.2025.22096
• Enlaces
  • Texto completo
• Resumen

  • In this paper we introduce the almost strongly star-Menger property and we provide some results and relationships with another known properties in literature. Furthermore, we characterize the almost strongly star-Menger and the almost star-Menger properties in hyperspaces endowed with the hit-and-miss topology $\tau_\Delta$, by using two new selection principles $\mathbf{S}_{\textsf{fin}}^{\star}(\Pi_{\Delta}(\Lambda), \mathscr{B})$ and $\mathbf{SS}_{\textsf{fin}}^{\star}(\Pi_{\Delta}(\Lambda), \mathscr{B})$, for an appropriate family $\mathscr{B}$.

• Referencias bibliográficas
  • P. S. Alexandroff and P. S. Urysohn, Mémoire sur les espaces topologiques compacts, Verh. Akad. Wetensch. Amsterdam 14 (1929), 1-96.
  • P. Bal and S. Bhowmik, Some new star-selection principles in topology, Filomat 31, no. 13 (2017), 4041-4050. https://doi.org/10.2298/FIL1713041B
  • M. Bonanzinga, F. Cammaroto, Lj. D. R. Kočinac and M.V. Matveev, On weaker forms of Menger, Rothberger and Hurewicz properties, Math. Vesnik...
  • M. Bonanzinga, D. Giacopello and F. Maesano, Some properties defined by relative versions of star-covering properties II, Appl. Gen. Topol....
  • M. Bonanzinga and F. Maesano, Some properties defined by relative versions of star-covering properties, Topol. Appl. 306, no. 1 (2020), 107923....
  • M. Bonanzinga and M.V. Matveev, Products of star-Lindelöf and related spaces, Houston J. Math. 27, no. 1 (2001), 45-57.
  • E. Borel, Sur la classification des ensembles de mesure nulle, Bull. Soc. Math. de France 47 (1919), 97-125. https://doi.org/10.24033/bsmf.996
  • R. Cruz-Castillo, A. Ramírez-Páramo and J. F. Tenorio, Characterizations of weaker forms of the Rothberger and Menger properties in hyperspaces,...
  • R. Cruz-Castillo, A. Ramírez-Páramo and J. F. Tenorio, Characterizations of weakly star-type Rothberger and Menger properties in hyperspaces,...
  • R. Cruz-Castillo, A. Ramírez-Páramo and J. F. Tenorio, H-star-Lindelöf property and weaker versions, Topol. Appl. 350 (2024), 108911. https://doi.org/10.1016/j.topol.2024.108911
  • R. Cruz-Castillo, A. Ramírez-Páramo and J. F. Tenorio, Hurewicz and Hurewicz-type star selection principles for hit-and-miss topology, Filomat...
  • R. Cruz-Castillo, A. Ramírez-Páramo and J. F. Tenorio, Menger and Menger-type star selection principles for hit-and-miss topology, Topol....
  • R. Cruz-Castillo, A. Ramírez-Páramo and J. F. Tenorio, On weaker versions of R-star-Lindelöf and M-star-Lindelöf properties, Filomat 38, no....
  • R. Cruz-Castillo, A. Ramírez-Páramo and J. F. Tenorio, Star and strong star-type versions of Rothberger and Menger principles for hit-and-miss...
  • P. Daniels, Pixley-Roy spaces over subsets of the reals, Topol. Appl. 29 (1988), 93-106. https://doi.org/10.1016/0166-8641(88)90061-2
  • G. Di Maio, Lj. D. R. Kočinac and E. Meccariello, Selection principles and hyperspaces topologies, Topol. Appl. 153 (2005), 912-923. https://doi.org/10.1016/j.topol.2005.01.020
  • J. Díaz-Reyes, A. Ramírez-Páramo and J. F. Tenorio, Rothberger and Rothberger-type star selection principles on hyperspaces, Topol. Appl....
  • E. van Douwen, G. M. Reed, A. W. Roscoe and I. J. Tree, Star covering properties, Topol. Appl. 39 (1991), 79-103. https://doi.org/10.1016/0166-8641(91)90077-Y
  • R. Engelking, On the double circumference of Alexandroff, Bull. Acad. Pol. Sci. Ser. Astron. Math. Phys. 16, no. 8 (1968), 629-634.
  • J. Fell, Hausdorff topology for the closed subsets of a locally compact non-Hausdorff spaces, Proc. Amer. Math. Soc. 13 (1962), 472-476. https://doi.org/10.1090/S0002-9939-1962-0139135-6
  • F. Hausdorff, Grundzuge der Mengenlehre, Leipzig, 1914.
  • W. Hurewicz, Über eine Verallgemeinerung des Borelschen Theorems, Math. Z. 24 (1925), 401-421. https://doi.org/10.1007/BF01216792
  • W. Just, A. W. Miller, M. Scheepers and P. J. Szeptycki, The combinatorics of open covers II, Topol. Appl. 73 (1996), 241-266. https://doi.org/10.1016/S0166-8641(96)00075-2
  • D. Kocev, Almost Menger and related spaces, Mat. Vesnik 61, no. 2 (2009), 173-180.
  • Lj. D. R. Kočinac, On star selection principles theory, Axioms 12, no. 93 (2023), 1-15. https://doi.org/10.3390/axioms12010093
  • Lj. D. R. Kočinac, Star-Menger and related spaces, Publ. Math. Debrecen 55 (1999), 421-431. https://doi.org/10.5486/PMD.1999.2097
  • Lj. D. R. Kočinac, Star-Menger and related spaces II, Filomat 13 (1999), 129-140.
  • Lj. D. R. Kočinac, Star selection principles: A survey, Khayyam J. Math. 1 (2015), 82-106.
  • G. Kumar and B. K. Tyagi, Weakly strongly star-Menger spaces, CUBO, A Mathematical Journal 32, no. 2 (2021), 287-298. https://doi.org/10.4067/S0719-06462021000200287
  • Z. Li, Selection principles of the Fell topology and the Vietoris topology, Topol. Appl. 212 (2016), 90-104. https://doi.org/10.1016/j.topol.2016.09.008
  • M. V. Matveev, A survey on star covering properties, Topology Atlas (1998), Preprint No. 330.
  • K. Menger, Einige Überdeckungssätze der Punltmengenlehre, Sitzungsberichte Abt. 2a, Mathematik, Astronomie, Physik, Meteorologie und Mechanik...
  • E. Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 71 (1951), 152-182. https://doi.org/10.1090/S0002-9947-1951-0042109-4
  • B. A. Pansera, Weaker forms of the Menger property, Quaest. Math. 35 (2012), 161-169. https://doi.org/10.2989/16073606.2012.696830
  • D. Pompeiu, Sur la continuité des fonctions de variables complexes, Ann. Fac. Sci. de Toulouse: Mathématiques 2e Série 7, no. 3 (1905), 265-315....
  • H. Poppe, Eine Bemerkung über Trennungsaxiome in Räumen von abgeschlossenen Teilmengen topologisher Räume, Arch. Math. 16 (1965), 197-198....
  • A. Ramírez-Páramo and A. Romero-Morales, Rothberger/Lindelöf-type star selection principles for hit-and-miss topology, Houston J. Math. 48,...
  • F. Rothberger, Eine Verschärfung der Eigenschaft C, Fundam. Math. 30 (1938), 50-55. https://doi.org/10.4064/fm-30-1-50-55
  • M. Scheepers, Combinatorics of open covers I: Ramsey theory, Topol. Appl. 69 (1996), 31-62. https://doi.org/10.1016/0166-8641(95)00067-4
  • M. Scheepers, Combinatorics of open covers VI. Selectors for sequences of dense sets, Quaest. Math. 22, no. 1 (1999), 109-130. https://doi.org/10.1080/16073606.1999.9632063
  • M. Scheepers, Lusin sets, Proc. Amer. Math. Soc. 197 (1999), 251-257. https://doi.org/10.1090/S0002-9939-99-04512-8
  • Y. K. Song, Remarks on almost Rothberger spaces and weakly Rothberger spaces, Quaest. Math. 38, no. 3 (2015), 317-325. https://doi.org/10.2989/16073606.2014.981710
  • Y. K. Song, Remarks on strongly star-Menger spaces, Comment. Math. Univ. Carolin. 54, no. 1 (2013), 97-104.
  • Y. K. Song, Some remarks on almost Menger spaces and weakly Menger spaces, Publ. de l'Ins. Math. 98, no. 112 (2015), 193-198. https://doi.org/10.2298/PIM150513031S
  • Y. K. Song, Some remarks on almost star countable spaces, Studia Sci. Math. Hungar. 52, no. 1 (2015), 12-20. https://doi.org/10.1556/sscmath.52.2015.1.1295
  • L. Vietoris, Bereiche Zweiter Ordnung, Monatshefte für Mathematik und Physik 33 (1923), 49-62. https://doi.org/10.1007/BF01705590
  • L. Zsilinszky, Baire spaces and hyperspace topologies, Proc. Amer. Math. Soc. 124 (1996), 3175-3184. https://doi.org/10.1090/S0002-9939-96-03528-9