A uniform approach to normality for topological spaces

Ankit Gupta; Ratna Dev Sarma

doi:10.4995/agt.2016.3919

A uniform approach to normality for topological spaces

Ankit Gupta, Ratna Dev Sarma

DOI: https://doi.org/10.4995/agt.2016.3919

Abstract

$(\lambda, \mu)$-regularity and $(\lambda, \mu)$-normality are defined for generalized topological spaces. Several variants of normality existing in the literature turn out to be particular cases of $(\lambda, \mu)$-normality. Uryshon's lemma and Titze's extension theorem are discussed in the light of ($\lambda, \mu$)-normality.

Keywords

generalized topology; normality; regularity

Subject classification

2020 Mathematics Subject Classification

54A05; 54D10

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References

M. E. Abd EI-Monsef, R. A. Mahmoud and S. N. El-Deeb, $beta$-open sets and $beta-$continuous mappings, Bull. Fac. Sci. Assiut Univ. 12 (1966), 77-90.

A. Csázàr, Generalized open sets, Acta Math. Hungar. 75 (1997), 65-87. https://doi.org/10.1023/A:1006582718102

A. Csázàr, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), 351-357. https://doi.org/10.1023/A:1019713018007

A. Csázàr, Separation axioms for generalized topologies, Acta Math. Hungar. 104, no. 1-2 (2004), 63-69. https://doi.org/10.1023/B:AMHU.0000034362.97008.c6

C. Dorsett, Semi-$T_2$, semi-$R_1$ and semi-$R_0$ topological spaces, Ann. Soc. Sci. Bruxelles 92 (1978), 143-150.

A. K. Das, A note on spaces between normal and $kappa$-normal spaces, Filomat 27, no. 1 (2013), 85-88. https://doi.org/10.2298/FIL1301085D

E. Hatir, T. Noiri and S. Yükesl, A decomposition of continuity, Acta Math. Hungar. 70 (1996), 145-150. https://doi.org/10.1007/BF00113919

J. K. Kohli and A. K. Das, New normality axioms and decomposition of normality, Glasnik Mat. 37 (57) (2002), 163-173.

J. C. Kelly, Bitopological spaces, Proc. London Math. Soc. 13, no. 3, (1963), 71-89. https://doi.org/10.1112/plms/s3-13.1.71

N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36-41. https://doi.org/10.1080/00029890.1963.11990039

A. S. Mashhour, M. E. Abd EI-Monsef and S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. and Phys. Soc. Egypt 53 (1981), 47-53.

O. Njastad, On some classes of nearly open sets, Pacific J. Math.15 (1965), 961-970. https://doi.org/10.2140/pjm.1965.15.961

T. Noiri and E. Hatir, $Lambda$sp-sets and some weak separation axioms, Acta Math. Hungar. 103, no. 3 (2004), 225-232. https://doi.org/10.1023/B:AMHU.0000028409.42549.72

D. Peleg, A generalized closure and complement phenomenon, Discrete Math. 50 (1984), 285-293. https://doi.org/10.1016/0012-365X(84)90055-4

J. Tong, A decomposition of continuity, Acta Math. Hungar. 48 (1986), 11-15. https://doi.org/10.1007/BF01949045

J. Tong, A decomposition of continuity in topological spaces, Acta Math. Hungar. 54 (1989), 51-55. https://doi.org/10.1007/BF01950708

R. D. Sarma, On convergence in generalized topology, Int. J. Pure and Appl. Math. 60 (2010), 51-56.

R. D. Sarma, On extremally disconnected generalized topologies, Acta Math. Hungar. 134, no. 4 (2012), 583-588. https://doi.org/10.1007/s10474-011-0153-8

N. V. Velicko, $H$-closed topological spaces, Amer. Math. Soc.Transl. 78, no. 2 (1968), 103-118. https://doi.org/10.1090/trans2/078/05

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