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On $\beta_1-\mathcal{I}-$ Paracompact Spaces

Yıl 2019, Cilt: 7 Sayı: 1, 73 - 78, 15.04.2019

Öz

In this paper our aim is  to introduce  the  class of $\beta_1-$paracompact spaces in ideal topological spaces. Then, some fundamental properties of  $\beta_1-\mathcal{I}-$paracompact spaces are given. Also,   the  relationships between $\beta_1-\mathcal{I}-$paracompact spaces and  other types of paracompact spaces are studied .



Kaynakça

  • [1] AlJarrah, H. H., b1-paracompact spaces, J. Nonlinear Sci. Appl., Vol:9 (4) (2016).
  • [2] Al-Zoubi, K. Y., S-Paracompact Spaces, Acta Math. Hungar, 110(1-2) (2006), 165-174.
  • [3] Andrijevic, D., Semi-preopen sets, Mat. Vesnik, 38 (1986), 24-32.
  • [4] Arkhangelski, V.I. (1984). Ponomarev, Fundamentals of General Topology Problems and Exercises, Hindustan, India.
  • [5] Bourbaki, N., General Topology, Part I., Addison-Wesley, Reading, Mass, (1966).
  • [6] Carnahan, D., Locally nearly-compact spaces, Boll. Un. Mat. Ital., 6.1 (1972), 146–153.
  • [7] Dahmen, R., Smooth embeddings of the Long Line and other non-paracompact manifolds into locally convex spaces, Topology and its Applications, 202 (2016), 70-79.
  • [8] Demir, I. and Ozbakir O. B., On b-paracompact spaces, Filomat 27(6) (2013), 971-976.
  • [9] Dieudonne, J. A., Une generalisation des espaces compacts, J. Math. Pures. Appl., 23 (1944), 65-76.
  • [10] El-Monsef, M. A., El-Deeb, S. N. and Mahmoud, R. A., b􀀀open sets and b􀀀continuous mappings, Bull. Fac. Sci. Assiut Univ, 12(1) (1983), 77-90.
  • [11] El-Monsef, M. A., Geaisa, A. N. and Mahmoud, R. A., b􀀀regular spaces, In Proc. Math. Phys. Soc. Egypt, 60 (1985), 47-52.
  • [12] El-Monsef, M. A., Mahmoud, R. A. and Lashin, E. R., b􀀀closure and b􀀀interior, J. Fac. Ed. Ain Shams Univ, 10 (1986), 235-245.
  • [13] Gutev V., Strongly paracompact metrizable spaces, Colloq. Math. 2 (2016), 144.
  • [14] Hamlett, T. R., Rose, D. and Jankovic, D., Paracompactness with respect to an ideal, International Journal of Mathematics and Mathematical Sciences, 20(3) (1997), 433-442.
  • [15] Jankovic, D. and Hamlett, T. R., New topologies from old via ideals, The American Mathematical Monthly, 97(4) (1990), 295-310.
  • [16] Jankovic, D.S., A note on mappings of extremally disconnected spaces, Acta Math. Hungar. 46 (1985), 83–92.
  • [17] Kuratowski, K., Topology I, NewYork Academic Press., (1966).
  • [18] Mahmoud, R. A. and Abd El-Monsef, M. E., b-irresolute and b-topological invariant, Proc. Pakistan Acad. Sci. 27 (1990), 285- 296.
  • [19] Navalagi G.B., Semi-precontinuous functions and properties of generalized semi-preclosed sets in topological spaces, Int. J. Math. Sci., 29, 1.1. (2002), 85-98.
  • [20] Njastad, O., On some classes of nearly open sets, Pacific Journal of mathematics, 15(3) (1965), 961-970.
  • [21] Noiri, T., Completely continuous image of nearly paracompact space, Mat. Vesn., 29, 1.6 (1977), 59–64.
  • [22] Ravi, O., Kumarb, R. S. and Choudhic, A. H., Decompositions of pg-Continuity via Idealization, Journal of New Results in Science, (2014), 3(7).
  • [23] Ray, A. D. and Bhowmick, R., m-paracompact and qm-paracompact generalized topological spaces, Hacettepe Journal of Mathematics and Statistics 45 (2) (2016), 447-453.
  • [24] Renukadevi, V. and Sathiyasundari, N., Nearly Paracompactness with respect to an ideal, J. Adv. Math. Stud. 8 (2015), 18-39.
  • [25] Sanabria, J., Rosas, E., Carpintero, C., Salas-Brown, M. and Garcıa, O., S-Paracompactness in ideal topological spaces, Mat. Vesnik, 68(3) (2016), 192-203.
  • [26] Sathiyasundari, N. and Renukadevi, V., Paracompactness with respect to an ideal, Filomat 27(2) (2013), 333-339.
  • [27] Singal M.K. and Singal A.R., Almost-continuous mappings, Yokohama Math. J. I6 (1968), 63-73.
  • [28] Stone, A. H., Paracompactness and product spaces, Bulletin of the American Mathematical Society, 54(10) (1948), 977-982.
  • [29] Vaidyanathaswamy, R., The localisation theory in set-topology, In Proceedings of the Indian Academy of Sciences-Section, Springer India, 20, 1 (1944), 51-61.
  • [30] Willard, S., General topology, Addison-Wesley Publishing Company, (1970).
  • [31] Zahid, M. I., Para H-closed spaces, locally para H-closed spaces and their minimal topologies, Ph. D. Dissertation, Univ. of Pittsburgh, (1981).
Yıl 2019, Cilt: 7 Sayı: 1, 73 - 78, 15.04.2019

Öz

Kaynakça

  • [1] AlJarrah, H. H., b1-paracompact spaces, J. Nonlinear Sci. Appl., Vol:9 (4) (2016).
  • [2] Al-Zoubi, K. Y., S-Paracompact Spaces, Acta Math. Hungar, 110(1-2) (2006), 165-174.
  • [3] Andrijevic, D., Semi-preopen sets, Mat. Vesnik, 38 (1986), 24-32.
  • [4] Arkhangelski, V.I. (1984). Ponomarev, Fundamentals of General Topology Problems and Exercises, Hindustan, India.
  • [5] Bourbaki, N., General Topology, Part I., Addison-Wesley, Reading, Mass, (1966).
  • [6] Carnahan, D., Locally nearly-compact spaces, Boll. Un. Mat. Ital., 6.1 (1972), 146–153.
  • [7] Dahmen, R., Smooth embeddings of the Long Line and other non-paracompact manifolds into locally convex spaces, Topology and its Applications, 202 (2016), 70-79.
  • [8] Demir, I. and Ozbakir O. B., On b-paracompact spaces, Filomat 27(6) (2013), 971-976.
  • [9] Dieudonne, J. A., Une generalisation des espaces compacts, J. Math. Pures. Appl., 23 (1944), 65-76.
  • [10] El-Monsef, M. A., El-Deeb, S. N. and Mahmoud, R. A., b􀀀open sets and b􀀀continuous mappings, Bull. Fac. Sci. Assiut Univ, 12(1) (1983), 77-90.
  • [11] El-Monsef, M. A., Geaisa, A. N. and Mahmoud, R. A., b􀀀regular spaces, In Proc. Math. Phys. Soc. Egypt, 60 (1985), 47-52.
  • [12] El-Monsef, M. A., Mahmoud, R. A. and Lashin, E. R., b􀀀closure and b􀀀interior, J. Fac. Ed. Ain Shams Univ, 10 (1986), 235-245.
  • [13] Gutev V., Strongly paracompact metrizable spaces, Colloq. Math. 2 (2016), 144.
  • [14] Hamlett, T. R., Rose, D. and Jankovic, D., Paracompactness with respect to an ideal, International Journal of Mathematics and Mathematical Sciences, 20(3) (1997), 433-442.
  • [15] Jankovic, D. and Hamlett, T. R., New topologies from old via ideals, The American Mathematical Monthly, 97(4) (1990), 295-310.
  • [16] Jankovic, D.S., A note on mappings of extremally disconnected spaces, Acta Math. Hungar. 46 (1985), 83–92.
  • [17] Kuratowski, K., Topology I, NewYork Academic Press., (1966).
  • [18] Mahmoud, R. A. and Abd El-Monsef, M. E., b-irresolute and b-topological invariant, Proc. Pakistan Acad. Sci. 27 (1990), 285- 296.
  • [19] Navalagi G.B., Semi-precontinuous functions and properties of generalized semi-preclosed sets in topological spaces, Int. J. Math. Sci., 29, 1.1. (2002), 85-98.
  • [20] Njastad, O., On some classes of nearly open sets, Pacific Journal of mathematics, 15(3) (1965), 961-970.
  • [21] Noiri, T., Completely continuous image of nearly paracompact space, Mat. Vesn., 29, 1.6 (1977), 59–64.
  • [22] Ravi, O., Kumarb, R. S. and Choudhic, A. H., Decompositions of pg-Continuity via Idealization, Journal of New Results in Science, (2014), 3(7).
  • [23] Ray, A. D. and Bhowmick, R., m-paracompact and qm-paracompact generalized topological spaces, Hacettepe Journal of Mathematics and Statistics 45 (2) (2016), 447-453.
  • [24] Renukadevi, V. and Sathiyasundari, N., Nearly Paracompactness with respect to an ideal, J. Adv. Math. Stud. 8 (2015), 18-39.
  • [25] Sanabria, J., Rosas, E., Carpintero, C., Salas-Brown, M. and Garcıa, O., S-Paracompactness in ideal topological spaces, Mat. Vesnik, 68(3) (2016), 192-203.
  • [26] Sathiyasundari, N. and Renukadevi, V., Paracompactness with respect to an ideal, Filomat 27(2) (2013), 333-339.
  • [27] Singal M.K. and Singal A.R., Almost-continuous mappings, Yokohama Math. J. I6 (1968), 63-73.
  • [28] Stone, A. H., Paracompactness and product spaces, Bulletin of the American Mathematical Society, 54(10) (1948), 977-982.
  • [29] Vaidyanathaswamy, R., The localisation theory in set-topology, In Proceedings of the Indian Academy of Sciences-Section, Springer India, 20, 1 (1944), 51-61.
  • [30] Willard, S., General topology, Addison-Wesley Publishing Company, (1970).
  • [31] Zahid, M. I., Para H-closed spaces, locally para H-closed spaces and their minimal topologies, Ph. D. Dissertation, Univ. of Pittsburgh, (1981).
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Elif Turanlı

Oya Bedre Özbakır Bu kişi benim

Yayımlanma Tarihi 15 Nisan 2019
Gönderilme Tarihi 6 Aralık 2018
Kabul Tarihi 18 Mart 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 7 Sayı: 1

Kaynak Göster

APA Turanlı, E., & Bedre Özbakır, O. (2019). On $\beta_1-\mathcal{I}-$ Paracompact Spaces. Konuralp Journal of Mathematics, 7(1), 73-78.
AMA Turanlı E, Bedre Özbakır O. On $\beta_1-\mathcal{I}-$ Paracompact Spaces. Konuralp J. Math. Nisan 2019;7(1):73-78.
Chicago Turanlı, Elif, ve Oya Bedre Özbakır. “On $\beta_1-\mathcal{I}-$ Paracompact Spaces”. Konuralp Journal of Mathematics 7, sy. 1 (Nisan 2019): 73-78.
EndNote Turanlı E, Bedre Özbakır O (01 Nisan 2019) On $\beta_1-\mathcal{I}-$ Paracompact Spaces. Konuralp Journal of Mathematics 7 1 73–78.
IEEE E. Turanlı ve O. Bedre Özbakır, “On $\beta_1-\mathcal{I}-$ Paracompact Spaces”, Konuralp J. Math., c. 7, sy. 1, ss. 73–78, 2019.
ISNAD Turanlı, Elif - Bedre Özbakır, Oya. “On $\beta_1-\mathcal{I}-$ Paracompact Spaces”. Konuralp Journal of Mathematics 7/1 (Nisan 2019), 73-78.
JAMA Turanlı E, Bedre Özbakır O. On $\beta_1-\mathcal{I}-$ Paracompact Spaces. Konuralp J. Math. 2019;7:73–78.
MLA Turanlı, Elif ve Oya Bedre Özbakır. “On $\beta_1-\mathcal{I}-$ Paracompact Spaces”. Konuralp Journal of Mathematics, c. 7, sy. 1, 2019, ss. 73-78.
Vancouver Turanlı E, Bedre Özbakır O. On $\beta_1-\mathcal{I}-$ Paracompact Spaces. Konuralp J. Math. 2019;7(1):73-8.
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