It's very unusual post here but still I'm asking you. My teacher has given me a project on semi open sets and regarding Topology. He advised me to read "Semi open sets and semi continuity on Topological Space" by Norman Levine, "Semi open sets" by W. J. M. Thomas, "A correction to the paper semi open sets and semi continuity in Topological Space" by Norman Levine by TR Hamlett, "On semi open sets with respect to an Ideal" by Friday Ifeanyi Michael.
After reading those papers my teacher told me to write down those papers according to my knowledge and understanding and submit it. But it's not quite interesting to me as I haven't solved any particular problems on semi open set, semi continuity, semi open set with respect to an Ideal. So to make my project work more superior I want to add some problems solving by me. It's my request to you to give me some problems relevant to that topics, I will try to solve. Thanks for reading.
There really aren't a lot of such exercises. No books that I have cover semi-open sets. It' s a really marginal subject, that few people work in. The few papers there are just try to generalize classical results on open sets to semi-open (or other "generalized open sets"), or refute such generalisations. It's IMHO just a way to produce "papers" of little depth or interest; so far I haven't seen any results or coherent theory on these notions that is of interest to anyone except authors of other papers on semi-openness. It's a dead topic of general topology that basically nobody cares about (your teacher being one of the exceptions).