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

Year 2019, Volume: 7 Issue: 1, 73 - 78, 15.04.2019

Elif Turanlı , Oya Bedre Özbakır

Abstract

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 .



Keywords

paracompact $\beta-$open set $\beta_1-$paracompact $\mathcal{I}-$paracompact

References

  • [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).

Year 2019, Volume: 7 Issue: 1, 73 - 78, 15.04.2019

Elif Turanlı , Oya Bedre Özbakır

Abstract

References

  • [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).
There are 31 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Research Article
Authors

Elif Turanlı

Oya Bedre Özbakır This is me

Publication Date April 15, 2019
Submission Date December 6, 2018
Acceptance Date March 18, 2019
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

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. April 2019;7(1):73-78.
Chicago Turanlı, Elif, and Oya Bedre Özbakır. “On $\beta_1-\mathcal{I}-$ Paracompact Spaces”. Konuralp Journal of Mathematics 7, no. 1 (April 2019): 73-78.
EndNote Turanlı E, Bedre Özbakır O (April 1, 2019) On $\beta_1-\mathcal{I}-$ Paracompact Spaces. Konuralp Journal of Mathematics 7 1 73–78.
IEEE E. Turanlı and O. Bedre Özbakır, “On $\beta_1-\mathcal{I}-$ Paracompact Spaces”, Konuralp J. Math., vol. 7, no. 1, pp. 73–78, 2019.
ISNAD Turanlı, Elif - Bedre Özbakır, Oya. “On $\beta_1-\mathcal{I}-$ Paracompact Spaces”. Konuralp Journal of Mathematics 7/1 (April2019), 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 and Oya Bedre Özbakır. “On $\beta_1-\mathcal{I}-$ Paracompact Spaces”. Konuralp Journal of Mathematics, vol. 7, no. 1, 2019, pp. 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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