New topologies between the usual and Niemytzki

Authors

  • Dina Abuzaid King Abdulaziz University
  • Maha Alqahtani Kinq Khalid University
  • Lutfi Kalantan King Abdulaziz University

DOI:

https://doi.org/10.4995/agt.2020.12042

Keywords:

Generated topology, H-space, Niemytzki plane, usual metric, CC-normal, L-normal, S-normal, C-paracompactness

Abstract

We use the technique of Hattori to generate new topologies on the closed upper half plane which lie between the usual metric topology and the  Niemytzki topology. We study some of their fundamental properties and weaker versions of normality.

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Author Biographies

Dina Abuzaid, King Abdulaziz University

Department of Mathematics

Maha Alqahtani, Kinq Khalid University

Department of Mathematics

Lutfi Kalantan, King Abdulaziz University

Department of Mathematics

References

S. AlZahrani and L. Kalantan. $C$-normal topological property, Filomat 31(2017), 407-411. https://doi.org/10.2298/FIL1702407A

V.A. Chatyrko and Y. Hattori, On reversible and bijectively related topological spaces, Topology and its Applications 201(2016), 432-440. https://doi.org/10.1016/j.topol.2015.12.052

R. Engelking, General Topology, Vol. 6, Berlin: Heldermann (Sigma series in pure mathematics) Poland, 1989.

O. Frink, Compactification and semi-normal spaces, Amer. J. Math. 86(1964), 602-607. https://doi.org/10.2307/2373025

G. Gruenhage, Generalized metric spaces, K. Kunen, J. E. Vaughan (Eds.), Handbook of set-Theoretic Topology, North-Holland, Amsterdam, 1984, pp. 423-510. https://doi.org/10.1016/B978-0-444-86580-9.50013-6

Y. Hattori, Order and topological structures of posets of the formal Balls on metric spaces, Mem. Fac. Sci. Eng. Shimane Univ. Ser. B Math Sci 43(2010), 13-26.

F.B. Jones, Concerning normal and completely normal spaces, Bull. Amer. Math. Soc. 43(1937), 671-677. https://doi.org/10.1090/S0002-9904-1937-06622-5

L. Kalantan, Results about k-normality, Topol Appl 125(2002) 47-62. https://doi.org/10.1016/S0166-8641(01)00258-9

L. Kalantan and M. Alhomieyed, CC-normal topological spaces, Turk J Math 41(2017), 749-755. https://doi.org/10.3906/mat-1604-3

L. Kalantan and M. Alhomieyed, S-normality, J. Math. Anal., v9,5(2018), 48-54.

L. Kalantan and M. M. Saeed, L-normality, Topology Proceedings, 50(2017), 141-149.

L. Kalantan, M. Saeed and H. Alzumi, C-paracompactness and C2-paracompactness, Turk. J. Math. Vol. 43, 1(2019), 9-20. https://doi.org/10.3906/mat-1804-54

J. Kulesza, Results on spaces between the Sorgenfrey and usual topologies, Topology and its Applications, 231(2017) 266-275. https://doi.org/10.1016/j.topol.2017.09.028

E. V. Shchepin, Real valued functions and spaces close to normal, Sib. J. Math. 13(1972), 1182-1196. https://doi.org/10.1007/BF00968394

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Published

2020-04-03

How to Cite

[1]
D. Abuzaid, M. Alqahtani, and L. Kalantan, “New topologies between the usual and Niemytzki”, Appl. Gen. Topol., vol. 21, no. 1, pp. 71–79, Apr. 2020.

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Articles