Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2022, Cilt: 51 Sayı: 1, 1 - 7, 14.02.2022

Memet Kule

https://doi.org/10.15672/hujms.911145

Öz

Kaynakça

  • [1] M.E. Abd El-Monsef, S.N. El-Deeb and R.A. Mahmoud, $\beta $ -open sets and $\beta $-continuous mappings, Bull. Fac. Sci., Assiut Univ. 12, 77-90, 1983.
  • [2] M.E. Abd El-Monsef and A.M. Kozae, Some generalized forms of compactness and closedness, Delta J. Sci. 9 (2), 257-269, 1985.
  • [3] D. Andrijević, Semi-preopen sets, Mat. Vesnik, 38, 24-32, 1986.
  • [4] Aqsa and M.U.D. Khan, On nearly Menger and nearly star Menger spaces, Filomat, 33, 6219-6227, 2019.
  • [5] M. Caldas and S. Jafari, A new decomposition of $\beta $ -open functions, Chaos Solitons Fractals 40, 10-12, 2009.
  • [6] D. Chodounsky, D. Repovs and L. Zdomskyy, Mathias forcing and combinatorial covering properties of filters, J. Symb. Log. 80, 1398-1410, 2015.
  • [7] M. Ganster and D. Andrijević, On some questions concerning semi-preopen sets, J. Inst. Math. & Comp. Sci. (Math. Ser.) 1 (2), 65-75, 1988.
  • [8] W. Hurewicz, Über die Verallgemeinerung des Borelschen Theorems, Math. Z. 24, 401-425, 1925.
  • [9] W. Hurewicz, Über Folgen stetiger Functionen, Fund. Math. 9, 193-204, 1927.
  • [10] L.D.R. Kocinac, The Pixley-Roy topology and selection principles, Questions Answers Gen. Topology. 19, 219-225, 2001.
  • [11] L.D.R. Kocinac, Selected results on selection principles. Proceedings of the 3rd Semi- nar on Geometry & Topology, 71-104, Azarb. Univ. Tarbiat Moallem, Tabriz, 2004.
  • [12] L.D.R. Kocinac, Generalized open sets and selection properties, Filomat, 33, 1485- 1493, 2019.
  • [13] L.D.R. Kocinac, Variations of classical selection principles: An overview, Quaest. Math., 43 (8), 1121-1153, 2020.
  • [14] L.D.R. Kocinac, A. Sabah, M.U.D. Khan and D. Seba, Semi-Hurewicz spaces, Hacet. J. Math. Stat. 46 (1), 53-66, 2017.
  • [15] L.D.R. Kocinac and M. Scheepers, Combinatorics of open covers (VII): Groupability, Fund. Math. 179 (2), 131-155, 2003.
  • [16] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70, 36-41, 1963.
  • [17] A.S. Mashour, M.E. Abd El-Monsef and S.N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53, 47-53, 1982.
  • [18] K. Menger, Einige Überdeckungssätze der Punktmengenlehre, Sitzungsberichte Abt. 2a, Mathematik, Astronomie, Physik, Meteorologie und Mechanik (Wiener Akademie, Wien) 133, 421-444, 1924.
  • [19] A. Sabah, M.U.D. Khan and L.D.R. Ko˘cinac, Covering properties defined by semi- open sets, J. Nonlinear Sci. Appl. 9 (6), 4388-4398, 2016.
  • [20] M. Sakai, The weak Hurewicz property of Pixley-Roy hyperspaces, Topology Appl. 160, 2531-2537, 2013.
  • [21] M. Scheepers, Combinatorics of open covers I: Ramsey theory, Topology Appl. 69, 31-62, 1996.
  • [22] M. Scheepers, Selection principles and covering properties in topology, Note Mat. 22 (2), 3-41, 2003.
  • [23] L.A. Steen and J.A. Seebach, Counterexamples in Topology, Holt, Rinehart and Win- ston, Inc., New York, 1970.
  • [24] B. Tsaban, Selection principles and special sets of reals, Open Problems in Topology II (E. Pearl, editor), Elsevier Science Publishing, Amsterdam, 91–108, 2007.
  • [25] B.K. Tyagi, S. Singh and M. Bhardwaj, Covering properties defined by preopen sets, Asian-European Journal of Mathematics, 14 (3), 2150035, 2021.

$\beta$-Menger and $\beta$-Hurewicz spaces

Yıl 2022, Cilt: 51 Sayı: 1, 1 - 7, 14.02.2022

Memet Kule

https://doi.org/10.15672/hujms.911145

Öz

Recently, some papers on weaker forms of classical covering properties of Hurewicz and Menger have been published. In this paper, using the covers formed by $\beta $-open sets, we introduce and study the properties of $\beta $-Menger and $\beta $-Hurewicz topological spaces. We give counterexamples that show the interrelations between those properties. The subject of our investigation is also the preservation of $\beta $-Menger and $\beta $-Hurewicz properties under subspaces, products, and mappings.

Anahtar Kelimeler

β-open set β-Menger space β-Hurewicz space

Kaynakça

  • [1] M.E. Abd El-Monsef, S.N. El-Deeb and R.A. Mahmoud, $\beta $ -open sets and $\beta $-continuous mappings, Bull. Fac. Sci., Assiut Univ. 12, 77-90, 1983.
  • [2] M.E. Abd El-Monsef and A.M. Kozae, Some generalized forms of compactness and closedness, Delta J. Sci. 9 (2), 257-269, 1985.
  • [3] D. Andrijević, Semi-preopen sets, Mat. Vesnik, 38, 24-32, 1986.
  • [4] Aqsa and M.U.D. Khan, On nearly Menger and nearly star Menger spaces, Filomat, 33, 6219-6227, 2019.
  • [5] M. Caldas and S. Jafari, A new decomposition of $\beta $ -open functions, Chaos Solitons Fractals 40, 10-12, 2009.
  • [6] D. Chodounsky, D. Repovs and L. Zdomskyy, Mathias forcing and combinatorial covering properties of filters, J. Symb. Log. 80, 1398-1410, 2015.
  • [7] M. Ganster and D. Andrijević, On some questions concerning semi-preopen sets, J. Inst. Math. & Comp. Sci. (Math. Ser.) 1 (2), 65-75, 1988.
  • [8] W. Hurewicz, Über die Verallgemeinerung des Borelschen Theorems, Math. Z. 24, 401-425, 1925.
  • [9] W. Hurewicz, Über Folgen stetiger Functionen, Fund. Math. 9, 193-204, 1927.
  • [10] L.D.R. Kocinac, The Pixley-Roy topology and selection principles, Questions Answers Gen. Topology. 19, 219-225, 2001.
  • [11] L.D.R. Kocinac, Selected results on selection principles. Proceedings of the 3rd Semi- nar on Geometry & Topology, 71-104, Azarb. Univ. Tarbiat Moallem, Tabriz, 2004.
  • [12] L.D.R. Kocinac, Generalized open sets and selection properties, Filomat, 33, 1485- 1493, 2019.
  • [13] L.D.R. Kocinac, Variations of classical selection principles: An overview, Quaest. Math., 43 (8), 1121-1153, 2020.
  • [14] L.D.R. Kocinac, A. Sabah, M.U.D. Khan and D. Seba, Semi-Hurewicz spaces, Hacet. J. Math. Stat. 46 (1), 53-66, 2017.
  • [15] L.D.R. Kocinac and M. Scheepers, Combinatorics of open covers (VII): Groupability, Fund. Math. 179 (2), 131-155, 2003.
  • [16] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70, 36-41, 1963.
  • [17] A.S. Mashour, M.E. Abd El-Monsef and S.N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt 53, 47-53, 1982.
  • [18] K. Menger, Einige Überdeckungssätze der Punktmengenlehre, Sitzungsberichte Abt. 2a, Mathematik, Astronomie, Physik, Meteorologie und Mechanik (Wiener Akademie, Wien) 133, 421-444, 1924.
  • [19] A. Sabah, M.U.D. Khan and L.D.R. Ko˘cinac, Covering properties defined by semi- open sets, J. Nonlinear Sci. Appl. 9 (6), 4388-4398, 2016.
  • [20] M. Sakai, The weak Hurewicz property of Pixley-Roy hyperspaces, Topology Appl. 160, 2531-2537, 2013.
  • [21] M. Scheepers, Combinatorics of open covers I: Ramsey theory, Topology Appl. 69, 31-62, 1996.
  • [22] M. Scheepers, Selection principles and covering properties in topology, Note Mat. 22 (2), 3-41, 2003.
  • [23] L.A. Steen and J.A. Seebach, Counterexamples in Topology, Holt, Rinehart and Win- ston, Inc., New York, 1970.
  • [24] B. Tsaban, Selection principles and special sets of reals, Open Problems in Topology II (E. Pearl, editor), Elsevier Science Publishing, Amsterdam, 91–108, 2007.
  • [25] B.K. Tyagi, S. Singh and M. Bhardwaj, Covering properties defined by preopen sets, Asian-European Journal of Mathematics, 14 (3), 2150035, 2021.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Memet Kule 0000-0002-2869-2358

Yayımlanma Tarihi 14 Şubat 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 51 Sayı: 1

Kaynak Göster

APA Kule, M. (2022). $\beta$-Menger and $\beta$-Hurewicz spaces. Hacettepe Journal of Mathematics and Statistics, 51(1), 1-7. https://doi.org/10.15672/hujms.911145
AMA Kule M. $\beta$-Menger and $\beta$-Hurewicz spaces. Hacettepe Journal of Mathematics and Statistics. Şubat 2022;51(1):1-7. doi:10.15672/hujms.911145
Chicago Kule, Memet. “$\beta$-Menger and $\beta$-Hurewicz Spaces”. Hacettepe Journal of Mathematics and Statistics 51, sy. 1 (Şubat 2022): 1-7. https://doi.org/10.15672/hujms.911145.
EndNote Kule M (01 Şubat 2022) $\beta$-Menger and $\beta$-Hurewicz spaces. Hacettepe Journal of Mathematics and Statistics 51 1 1–7.
IEEE M. Kule, “$\beta$-Menger and $\beta$-Hurewicz spaces”, Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 1, ss. 1–7, 2022, doi: 10.15672/hujms.911145.
ISNAD Kule, Memet. “$\beta$-Menger and $\beta$-Hurewicz Spaces”. Hacettepe Journal of Mathematics and Statistics 51/1 (Şubat 2022), 1-7. https://doi.org/10.15672/hujms.911145.
JAMA Kule M. $\beta$-Menger and $\beta$-Hurewicz spaces. Hacettepe Journal of Mathematics and Statistics. 2022;51:1–7.
MLA Kule, Memet. “$\beta$-Menger and $\beta$-Hurewicz Spaces”. Hacettepe Journal of Mathematics and Statistics, c. 51, sy. 1, 2022, ss. 1-7, doi:10.15672/hujms.911145.
Vancouver Kule M. $\beta$-Menger and $\beta$-Hurewicz spaces. Hacettepe Journal of Mathematics and Statistics. 2022;51(1):1-7.

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