Countable Paracompactness of Nano Topological Space Modeled by Pre-open Sets Structures
DOI:
https://doi.org/10.31642/JoKMC/2018/110106%20Keywords:
Nano Topology , Pararcompact Spaces , Regular Space , Normal Space , Pre-open , Separation Axioms, Countable Nano Pre-open ParacompactAbstract
A new class of paracompactness in the nano topological spaces, termed nano pre open sets, are presented and explored in this article. Since the Nano topology contains at most five sets this leads us to establish new structures of nano open sets, nano open covers, and nano locally refinement coves new requirement concepts are discussed like Nano pre open covers, Nano pre , , , and Nano pre- regular, Nano pre-normal spaces, and Countable Nano Pre-open Paracompact. Many new theorems are stated and proved.
Downloads
References
Abdulkadhum, Aljariawi Salam, and Z. D. Al-Nafie. "On
Paracompactness of the Space CLipk (Ω)." Journal of Physics:
Conference Series. Vol. 1804. No. 1. IOP Publishing, 2021.
Al Nafie, Z.D., Mera, A. "A new method for exisience ofa
Lip k" .Journal of Advanced Research in Dynamical and
Control Systems,v )2018(, 10(10), pp. 156-158.
Al Nafie, Z. D. "Partition of a unity on infinite-dimensional
manifold of the Lipschiz class Lip k." Russian Mathematics
(2017): 5-10.
Dhanasekaran, P., Kumar, C. V., Sathishmohan, P.,
Rajendran, V. "Some Normalities in Forms of Nano
Topological Spaces. "Advances in Mathematics 9(2020):[5] Dieudonné, Jean. "Une généralisation des espaces
compacts." Journal de Mathématiques Pures et Appliquées
(1944): 65-76.
Dowker, Clifford H. "On countably paracompact spaces.
" Canadian Journal of Mathematics 3 (1951): 219-224.
El-Atik, Abd El-Fattah A., and Hanan Z. Hassan.
"Some nano topological structures via ideals and graphs.
" Journal of the Egyptian Mathematical Society 28.1 (2020):
-21.
Engelking, Ryszard. "General topology" Sigma series in
pure mathematics 6 (1989).
Katětov, Miroslav. "On real-valued functions in topological
spaces." Fundamenta Mathematicae 1.38 (1951): 85-91.
Mashhour, A. S., ME Abd El-Monsef, and I. A. Hasanein.
"On pretopological spaces." Bulletin Mathematique de la
Societe
des Sciences Mathematiques de la Republique Socialiste
de roumanie (1984): 39-45.
Mashhour, A. S. "On precontinuous and weak
precontinuous mappings." Proc. Math. Phys. Soc. Egypt..
Vol. 53. 1982.
Pawlak, Zdzisław. "Rough sets." International
journal of
computer & information sciences 11 (1982): 341-356.
Sathishmohan, P., et al. "More on nano pre-neighbourhoods in nano topological-spaces." Journal of Applied Science and Computations 5.11 (2018): 899-907.
Sathishmohan, P., Rajendran, V., & Dhanasekaran, P. K. (2019). "Further properties of nano pre-$ T_0 $, nano pre-$ T_1 $ and nano pre-$ T_2 $ spaces. " Malaya Journal of Matematik, 7(01), 34-38.
Thivagar, M. Lellis, and Carmel Richard. "Note on
nano topological spaces." Communicated 1.2.2 (2014): 2-3.
Thivagar, M. Lellis and Carmel Richard. "On nano
forms of weakly open sets." International journal of mathematics
and Statistics Invention 1.1 (2013): 31-37.
Downloads
Published
How to Cite
Issue
Section
Categories
License
Copyright (c) 2024 Ghufran Jalaukhan, Z.D AL-Nafie
This work is licensed under a Creative Commons Attribution 4.0 International License.
which allows users to copy, create extracts, abstracts, and new works from the Article, alter and revise the Article, and make commercial use of the Article (including reuse and/or resale of the Article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made and the licensor is not represented as endorsing the use made of the work.