I think funcoids are more important for mathematics than topological spaces. Why I think so? Because funcoids have “smoother” (more beautiful) properties than topological spaces.

Funcoids were discovered by me. Does the author mean that his discovery of funcoids was more important than the discovery of topological spaces?

No. Either topological spaces or funcoids are necessary for describing properties of continuity in an abstract way. We already have a (I’d say a rather poor) way to describe continuity with topological spaces. With author’s discovery of funcoids we get a second way to do a similar thing. We already had one way and discovering a second way is less important. So the discovery of funcoids was a lesser discovery than the the discovery of topological spaces.

Funcoids are more important than topological spaces indeed. I hope the history of mathematics will remark this.