Abstract. In this work, some new concepts were introduced and the relationship between them was studied. These concepts are filter directed-toward, nano-closure-directed-toward and nano-closure-converge to point, and some theories and results about these concepts were presented. A definition almost-nano-converges for set, almost-nano-cluster-point, and definition of quasi-nano-Hausdorff-closed and was also called nano-Hausdorff-closed relative, were also presented several theories related to these definitions were presented and the relationship between them was studied . We also provided other generalizations, including nano closure continuous mappings and it was also called as nano-weaklycontinuous- mappings, as well as providing a definition of nano-compact-mappings, nano-rigid a set, almost-nano-closedmappings and, nano-Urysohn where several theories have been presented that have a relationship between these vital species and proved it is main results. Finally, the filter bases presented quite a few theories and results related to nanoperfect- mappings, which summed up three conditions under one condition, i.e. considered another definition of the nanoperfect- mappings by the filter bases.
