Introducing selective d-separability in bitopological spaces

Özçağ, Selma

doi:10.55730/1300-0098.3257

Introducing selective d-separability in bitopological spaces

Selma ÖZÇAĞ (Hacettepe Üniversitesi, Fen Fakültesi, Matematik Bölümü, Ankara, Türkiye)

Turkish Journal of Mathematics

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Yıl: 2022 Cilt: 46 Sayı: 6 Sayfa Aralığı: 2109 - 2120 Metin Dili: İngilizce DOI: 10.55730/1300-0098.3257 İndeks Tarihi: 09-12-2022

Introducing selective d-separability in bitopological spaces

Öz:

We introduce D -separability and its game-theoretic version, $D^+$ -separability in bitopological spaces, and investigate their relationships with d -separability and a weaker form of H -separability which will be called DH - separability. Further we give the connection of these notions with the selective versions of separability-types properties under the bitopological context. We also obtain some results about the d -separability properties of bitopological spaces which are slightly different from those one expects for the classical case

Anahtar Kelime: Selection principles bitopological space D -separability selective separability

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Aurichi LF, Dias RR, Junqueira RL. On d- and D-separability. Topology and its Applications 2012; 159: 3445-3452.
[2] Bella A, Matveev M, Spadaro S. Variations of selective separability II: Discrete sets and the influence of convergence and maximality. Topology and its Applications 2012; 159: 253-271.
[3] Bennett HR. On quasi-developable spaces. General Topology and Applications 1971; 1: 253-262.
[4] Dow A, Tkachenko MG, Tkachuk VV, Wilson RG. Topologies generated by discrete subspaces. Glas.Mat.Ser.III 2002; 37: 189-212.
[5] Dvalishvili BP. Bitopological Spaces: Theory, Relations with Generalized Algebraic Structures and Applications, North Holland Mathematics Studies, Elsevier, 2005.
[6] Engelking R. General Topology. Heldermann-Verlag, Berlin, 1989.
[7] Eysen AE, Özçağ S. Games relating to weak covering properties in bitopological spaces. Turkish Journal of Mathematics 2020; 44 (6): 2297-2305.
[8] Gruenhage G. Generalized metric spaces, in: K. Kunen, J.E. Vaughan (Eds.), Handbook of Set-Theoretic Topology, Elsevier, 423-501, 1984.
[9] Juhász I, Soukup L. and Szentmiklóssy Z. Resolvability and monotone normality. Israel Journal of Mathematics 2008; 166: 116.
[10] Kelly JC. Bitopological spaces. Proceedings of the London Mathematical Society 1963; 3 (13): 71-89.
[11] Kočinac, L. Variations of classical selection principles: An overview. Quaestiones Mathematicae 2020; 43 (8): 1121-1153.
[12] Kočinac L, Özçağ S. Versions of separability in bitopological spaces. Topology and its Applications 2011; 158 (12): 1471-1477.
[13] Kočinac L, Özçağ S. Bitopological spaces and selection principles. Proceedings ICTA 2011 (Islamabad, Pakistan, July 4-10, 2011), Cambridge Scientific Publishers, 2012; 243-255.
[14] Kočinac L, Özçağ S. More on selective covering properties in bitopological spaces. Journal of Mathematics, 2021, Article ID 5558456, 9 pages.
[15] Kurepa, G. Le probleme de Souslin et les espaces abstraits, Comptes rendus de l’Académie des Sciences Paris 1936; 203: 1049-1052 (in French).
[16] Lyakhovets D, Osipov AV. Selection principles and games in bitopological function spaces. Filomat 2019; 33 (14): 4535-4540.
[17] Menger K. Einige Überdeckungssätze der Punktmengenlehre, Sitzungsberichte Abt. 2a, Mathematik, Astronomie, Physik, Meteorologie und Mechanik (Wiener Akademie, Wien) 1924; 133: 421-444 (in German).
[18] Osipov AV, Özçaǧ S. Variations of selective separability and tightness in function spaces with set-open topologies. Topology and its Applications 2017; 217: 38-50.
[19] Özçağ S. Selective bitopological versions of separability. Topology and its Applications 2016; 201: 403-413.
[20] Rothberger F. Eine Verscharfung der Eigenschaft C. Fundamenta Mathematicae 1938; 30: 50-55 (in German).
[21] Sakai M, Scheepers M. The combinatorics of open covers, In: K.P. Hart, J. van Mill, P. Simon (eds.), Recent Progress in General Topology III. Atlantis Press 2014; 751-800.
[22] Scheepers M. Combinatorics of open covers (I): Ramsey theory. Topology and its Applications 1996; 69(1): 31-62.
[23] Scheepers M. Combinatorics of open covers VI: Selectors for sequences of dense sets, Quaestiones Mathematicae 2005; 28: 409-424.
[24] Soukup D, Soukup L, Spadaro S. Comparing weak versions of separability. Topology and its Applications 2013; 160 (18): 2538-2566.
[25] Vaughan JE. Two spaces homeomorphic to Seq(p). Commentationes Mathematicae Universitatis Carolinae 2001; 42: 209-218.

APA	Özçağ S (2022). Introducing selective d-separability in bitopological spaces. , 2109 - 2120. 10.55730/1300-0098.3257
Chicago	Özçağ Selma Introducing selective d-separability in bitopological spaces. (2022): 2109 - 2120. 10.55730/1300-0098.3257
MLA	Özçağ Selma Introducing selective d-separability in bitopological spaces. , 2022, ss.2109 - 2120. 10.55730/1300-0098.3257
AMA	Özçağ S Introducing selective d-separability in bitopological spaces. . 2022; 2109 - 2120. 10.55730/1300-0098.3257
Vancouver	Özçağ S Introducing selective d-separability in bitopological spaces. . 2022; 2109 - 2120. 10.55730/1300-0098.3257
IEEE	Özçağ S "Introducing selective d-separability in bitopological spaces." , ss.2109 - 2120, 2022. 10.55730/1300-0098.3257
ISNAD	Özçağ, Selma. "Introducing selective d-separability in bitopological spaces". (2022), 2109-2120. https://doi.org/10.55730/1300-0098.3257

APA	Özçağ S (2022). Introducing selective d-separability in bitopological spaces. Turkish Journal of Mathematics, 46(6), 2109 - 2120. 10.55730/1300-0098.3257
Chicago	Özçağ Selma Introducing selective d-separability in bitopological spaces. Turkish Journal of Mathematics 46, no.6 (2022): 2109 - 2120. 10.55730/1300-0098.3257
MLA	Özçağ Selma Introducing selective d-separability in bitopological spaces. Turkish Journal of Mathematics, vol.46, no.6, 2022, ss.2109 - 2120. 10.55730/1300-0098.3257
AMA	Özçağ S Introducing selective d-separability in bitopological spaces. Turkish Journal of Mathematics. 2022; 46(6): 2109 - 2120. 10.55730/1300-0098.3257
Vancouver	Özçağ S Introducing selective d-separability in bitopological spaces. Turkish Journal of Mathematics. 2022; 46(6): 2109 - 2120. 10.55730/1300-0098.3257
IEEE	Özçağ S "Introducing selective d-separability in bitopological spaces." Turkish Journal of Mathematics, 46, ss.2109 - 2120, 2022. 10.55730/1300-0098.3257
ISNAD	Özçağ, Selma. "Introducing selective d-separability in bitopological spaces". Turkish Journal of Mathematics 46/6 (2022), 2109-2120. https://doi.org/10.55730/1300-0098.3257