C - Compactness And Characterization Modulo An Ideal

R. Alagar; R. Thenmozhy

doi:https://doi.org/10.14445/22315373/IJMTT-V66I5P514

International Journal of Mathematics Trends and Technology

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Volume 66 | Issue 5 | Year 2020 | Article Id. IJMTT-V66I5P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I5P514

C - Compactness And Characterization Modulo An Ideal

R. Alagar , R. Thenmozhy

Abstract

An ideal on a set X is a non-empty collection of subsets of X with heredity property which is also closed under arbitrary union and finite intersections. In this paper, we introduce C - compactness with respect to ideal and discuss some of their properties. Also, this paper gives the characterizations of C compactness with respect to ideal, some of which make use of filter.

Keywords

F- Compact §- compact, §C - Compact, compatible ideal §.

References

[1] Hamlett, T.R and Dragan Jankovic: Compactness with respect to an ideal, Bollo . un. Mat. Ital. B(7) 4 (1990) 849 - 861.
[2] Jankovic, D. and Hamlett, T.R: New topologies from old via ideals, American Math monthly, 97, (1990), 295 - 310 .
[3] Newcomb, R.L.: Topologies which are compact modulo an ideal, Ph.D. Dissertation, Univ. of Cal. at Santa, Barbara, (1967).
[4] T. R. Hamlett, D. A. Rose; Topological properties, Int. J. Math Sci., 13(3),(1990), 507-512
[5] T. R. Hamlett, D. Jankovic; Ideals in topological and the set operator,. Boll UMI, 7(4-B) (1990), 863-974
[6] K. Kuratowski; Topology, Vol.1 (Academic Press, New york,1966)
[7] A. Nasef, E.Hatir; On pre-I-open sets and a decomposition of I - continuity, Chaos, Solitons & Fractals, 40 (2007), 1185-1189
[8] A. Nasef, R. A. Mahmoud; Some topological applications via ideals; Chaos, Solitons & Fractals, 13 (2002), 825-831
[9] T. Natkaniec; On I-continuity and I-semicontinuity points, Math. Slovaca,36(3) (1986), 297-312
[10] D.A.Rose, T. R. Hamlett; Ideally equivalent topologies and semi-topological properties, Math Chronicle, 20 (1991), 149-156
[11] Vaidyanathaswamy, R: Set topology, Chelsea publishing company, (1960 )
[12] Vaidyanathaswamy, R: The localization theory in set topology, Proc. Indian Acad. Sci., 20 (1945), 51 – 61.

Citation :

R. Alagar , R. Thenmozhy, "C - Compactness And Characterization Modulo An Ideal," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 5, pp. 99-105, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I5P514