I decided to sent the manuscript to Rejecta Mathematica. I submitted it to Rejecta Mathematica yesterday.
Previously I was going to study category theory and then rewrite my article in order to resubmit it to a reputable math journal, not Rejecta. The research to which the reviewer referred me uses category theory. But after reading some chapters of two category theory books, I yet see that my knowledge of category theory is yet weak. As such, I decided to abandon the attempt to understand these writings considering them out of reach and do my best to publish my article about connectedness of sets in Rejecta.
Me in the process of mathematical discoveries without advanced category theory is like David overcoming Goliath without serious military equipment just by a sling. In the same way I overcame the task of developing an entirely new math theory without knowledge of categories and other wise stuffs.
As well as David afterward learned to fight with sword, I also hope that in a future I will study related fields of math such as category theory. But now I have an awesome research success without it.