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).