On generalized preopen sets

A. Mukharjee; R. M. Roy

doi:10.15330/ms.51.1.195-199

Firstly in this paper, we find some conditions under which $\mu$-preopen sets of a GTS or $\mu$-space $X$ may be equivalent to $\mu$-open in $X$. Finally, we obtain some characterizations of generalized paracompactness of a GTS or $\mu$-space $X$ via $\mu$-preopen sets in $X$.

1. M.M. Arar, On countably $\mu$-paracompact spaces, Acta Math. Hungar., 149 (2016), №1, 50-57.

2. H.H. Corson and E. Michael, Metrizability of certain countable unions, Illinois J. Math., 8 (1964), 351-360.

3. A. Deb Ray, R. Bhowmick, $\mu$-paracompact and $g_{\mu}$-paracompact generalized topological spaces, Hacet. J. Math. Stat., 45 (2016), №1, 447-453.

4. A. Csaszar, Generalized open sets in generalized topologies, Acta Math. Hungar., 106 (2005), №1.2, 351-357.

5. A. Csaszar, Extremally disconnected generalized topologies, Ann. Univ. Sci. Budapest. Eotvos Sect. Math., 47 (2004), 91-96.

6. A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), №4, 351.357.

7. E. Ekici, Generalized Hyperconnectedness, Acta Math. Hungar., 133 (2011), №1-2, 140-147.

8. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41.

9. AS. Mashhour, M.E. Abd El-Monsef, S.N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phy. Soc. Egypt, 53 (1982), 47-53.

10. A. Mukharjee, A covering property with respect to generalized preopen sets, Bol. Soc. Paran. Mat., 38 (2002), №6, 25-32.

11. T. Noiri, Unified characterizations of modifications of $R_0$ and $R_1$ topological spaces, Rend. Circ. Mat. Palermo, (2) 55 (2006), 29-42.

12. S. Willard, General Topology, Addison-Wesley Publishing Company, Reading, 1970.

	On generalized preopen sets
Author	A. Mukharjee¹, R. M. Roy² ajoyjee@gmail.com¹, roy_rebati@rediffmail.com² 1) Department of Mathematics, St. Joseph’s College, Darjeeling, W. Bengal, India; 2) Department of Mathematics, Mathabhanga College, Coochbehar, W. Bengal, India
Abstract	Firstly in this paper, we find some conditions under which $\mu$-preopen sets of a GTS or $\mu$-space $X$ may be equivalent to $\mu$-open in $X$. Finally, we obtain some characterizations of generalized paracompactness of a GTS or $\mu$-space $X$ via $\mu$-preopen sets in $X$.
Keywords	$\mu$-preopen set; $\mu$-dense; $\mu$-locally finite; $\mu$-paracompact
DOI	doi:10.15330/ms.51.2.195-199
Reference	1. M.M. Arar, On countably $\mu$-paracompact spaces, Acta Math. Hungar., 149 (2016), №1, 50-57. 2. H.H. Corson and E. Michael, Metrizability of certain countable unions, Illinois J. Math., 8 (1964), 351-360. 3. A. Deb Ray, R. Bhowmick, $\mu$-paracompact and $g_{\mu}$-paracompact generalized topological spaces, Hacet. J. Math. Stat., 45 (2016), №1, 447-453. 4. A. Csaszar, Generalized open sets in generalized topologies, Acta Math. Hungar., 106 (2005), №1.2, 351-357. 5. A. Csaszar, Extremally disconnected generalized topologies, Ann. Univ. Sci. Budapest. Eotvos Sect. Math., 47 (2004), 91-96. 6. A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), №4, 351.357. 7. E. Ekici, Generalized Hyperconnectedness, Acta Math. Hungar., 133 (2011), №1-2, 140-147. 8. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41. 9. AS. Mashhour, M.E. Abd El-Monsef, S.N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phy. Soc. Egypt, 53 (1982), 47-53. 10. A. Mukharjee, A covering property with respect to generalized preopen sets, Bol. Soc. Paran. Mat., 38 (2002), №6, 25-32. 11. T. Noiri, Unified characterizations of modifications of $R_0$ and $R_1$ topological spaces, Rend. Circ. Mat. Palermo, (2) 55 (2006), 29-42. 12. S. Willard, General Topology, Addison-Wesley Publishing Company, Reading, 1970.
Pages	195-199
Volume	51
Issue	2
Year	2019
Journal	Matematychni Studii
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