New forms of compactness via grills

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2017 by IJMTT Journal
Volume-48 Number-4
Year of Publication : 2017
Authors : M. K. Gupta, Monika Gaur
  10.14445/22315373/IJMTT-V48P540

MLA

M. K. Gupta, Monika Gaur "New forms of compactness via grills", International Journal of Mathematics Trends and Technology (IJMTT). V48(4):270-275 August 2017. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

Abstract
In the present paper, we introduce and study new types of compactness with respect to a grill, namely ρG – compactness and σG – compactness. Several of its properties are investigated and effects of various kinds of functions on them are studied.

Reference
[1] Choquet, G., Sur les notions de filter et grille, Comptes Rendus Acad. Sci. Paris, 224(1947), 171-173.
[2] Gupta, M.K., and Noiri, T., C-compactness modulo an ideal, International J. Math. and Math. Sci., (2006), 1-12. DOI: 10.1155/IJMMS/2006/78135.
[3] Levin, N., Generalized closed sets in Topological spaces, Rend. Circ. Mat. Palermo, 19 (1970), 89-96.
[4] Newcomb, R.L., Topologies which are compact modulo an ideal, Ph.D. Dissertation, Univ. of Cal. at Santa Barbara, (1967).
[5] Pachόn, N.R., New forms of strong compactness in terms of ideals, Int. J. of Pure and App. Math., 106(2)(2016),481-493.DOI: 10.12732/ijpam.v106i2.12.
[6] Roy, B., and Mukherjee, M. N., On a typical topology induced by a grill, Soochow J. of Math., 33(4)(2007), 771-786.
[7] Roy, B., and Mukherjee, M.N., On a type of compactness via grills, Matematicki Vesnik, 59(2007), 113-120.

Keywords
Grill, G – compact, Gg– closed, ρG – compact, σG – compact.