Geodesic
A note on weak structures due to Császár
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2015), pp. 114-116 
A. K. Das. A note on weak structures due to Császár. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2015), pp. 114-116. http://geodesic.mathdoc.fr/item/BASM_2015_2_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Weak structures has been introduced by Á. Császár and it has been shown that every generalized topology and every minimal structure is a weak structure. Recently E. Ekici introduced and studied the structure $r(w)$ in a weak structure $w$ on $X$. In general the structure $r(w)$ need not be a topology on $X$. In this paper we have shown that under some conditions $r(w)$ is a topology on $X$. Further, comparision of two weak structures has been studied.

[1] Á. Császár, “Generalized open sets”, Acta Math. Hungar., 75:1–2 (1997), 65–87 | DOI | MR | Zbl

[2] Á. Császár, “Generalized topology, generalized continuity”, Acta Math. Hungar., 96:4 (2002), 351–357 | DOI | MR | Zbl

[3] Á. Császár, “Generalized open sets in generalized topologies”, Acta Math. Hungar., 106:1–2 (2005), 53–66 | MR | Zbl

[4] Á. Császár, “Weak structures”, Acta Math. Hungar., 131:1–2 (2011), 193–195 | DOI | MR | Zbl

[5] E. Ekici, “On weak structures due to Császár”, Acta Math. Hungar., 134:4 (2012), 565–570 | DOI | MR | Zbl