In this manuscript, it is aimed to convert the topology on a set X which is on a nearness approximation space to new set families via indiscernibility relation. Then, if the open sets of the present topology are defined as the set of related elements, the set families, which have weakly related elements, will be obtained. Finally, the topological properties and concepts that these new families hold will be examined.
HenryC., Near Sets: Theory andApplications (Ph.D. Thesis (supervisor J.F. Peters) Department of Electrical & Computer Engineering, University of Manitoba, (2010).
2.
İnanE. and ÖztürkM.A., Erratum and notes for near groups on nearness approximation spaces, Hacettepe Journal of Mathematics and Statistics43(2) (2014), 279–281.
3.
İnanE. and ÖztürkM.A., Near groups on nearness approximation spaces, Hacettepe Journal of Mathematics and Statistics41(4) (2012), 545–558.
4.
İnanE. and ÖztürkM.A., Near semigroups on nearness approximation spaces, Annals of Fuzzy Mathematics and Informatics10(2) (2015), 287–297.
5.
PetersJ.F., Near sets, General theory about nearness of objects, Applied Mathematical Sciences1(53–56) (2007), 2609–2629.
6.
PetersJ.F., Near sets, special theory about nearness of objects, Fundamenta Informaticae75(1–4) (2007), 407–433.
7.
PetersJ.F., Sufficiently near sets of neighbourhoods, Rough Sets and Knowledge Technology (2011), LNCS 6954, Springer, Berlin, 17–24.
8.
PetersJ.F. and NaimpallyS., Approach spaces for near filters, General Mathematical Notes2(1) (2011), 159–164.
9.
PetersJ.F. and TiwariS., Approach merotopies and near filters, General Mathematical Notes3(1) (2011), 1–15.
10.
WolskiM., Perception and classification, A note on near sets and rough sets, Fundamenta Informaticae101 (2010), 143–155.
11.
MashhourA.S., et al., On supra topological spaces, Indian J Pure Appl Math14(4) (1983), 502–510.
