The P-Hausdorff, P-regular and P-normal ideal spaces
DOI:
https://doi.org/10.22199/issn.0717-6279-2020-03-0043Keywords:
Separation in ideal topological spaces, Hausdorff modulo ℐ, ℐ-Hausdorff, ℐ-regular, ℐ normalAbstract
We introduce and study new extensions of some separation axioms to ideal topological spaces, which we have called P-Hausdorff, P-regular and P-normal. These extensions are quite natural and represent a good improvement with respect to other extensions that have recently occurred, in which a level of separation that can be considered acceptable is not perceived.
References
J. Dontchev, “On Hausdorff spaces via topological ideals and I-irresolute functions”, Annals of the New York Academy of Sciences, vol. 767, no. 1, pp. 28–38, Sep. 1995, doi: 10.1111/j.1749-6632.1995.tb55891.x
D. Janković and T.R. Hamlett, “Compatible extensions of ideals”, Unione Matematica Italiana Bollettino. B. Serie 7, vol. 6, no. 3, pp. 453-465, 1992.
D. Janković and T. R. Hamlett, “New topologies from old via ideals”, The american mathematical monthly, vol. 97, no. 4, pp. 295–310, Apr. 1990., doi: 10.1080/00029890.1990.11995593
T. R. Hamlett and D. Janković, “On weaker forms of paracompactness, countable compactness, and Lindelöfness”, Annals of the New York Academy of Sciences, vol. 728, no. 1, pp. 41–49, Nov. 1994, doi: 10.1111/j.1749-6632.1994.tb44132.x
R. Newcomb, "Topologies which are compact modulo an ideal", Ph.D. dissertation, University of California at Santa Barbara, 1967.
N. R. Pachón Rubiano, “Between closed and Ig-closed sets”, European journal of pure and applied mathematics, vol. 11, no. 1, p. 299, Jan. 2018, doi: 10.29020/nybg.ejpam.v11i2.3131
N.R. Pachón Rubiano, “Some properties of J -Hausdorff, J -regular and J - normal spaces”, Scientific studies and research. Series mathematics, vol. 28, no. 2, pp. 49-62, 2018. [On line]. Available: https://bit.ly/2TXJ1RN
V. Renuka Devi and D. Sivaraj, “A generalization of normal spaces”, Archivum mathematicum (Brno), vol. 44, pp. 265-270, 2008. [On line]. Available: https://bit.ly/36MDAud
D. Sivaraj and V. Renuka Devi, “Some separation axioms via ideals”, Bollettino dell'Unione Matematica Italiana, vol. 10-B, no. 3, pp. 917-931, 2007. [On line]. Available: https://bit.ly/3gGx9gH
S. Suriyakala and R. Vembu, “On separation axioms in ideal topological spaces”, Malaya journal of matematik, vol. 4 , no. 2, pp. 318-324, Apr. 2016. [On line]. Available: https://bit.ly/2Mf5XHN
R. Vaidyanathaswamy, “The localisation theory in set-topology”, Proceedings of the Indian Academy of Sciences - Section A, vol. 20, no. 1, pp. 51–61, Jul. 1944, doi: 10.1007/BF03048958
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