Strong \(B_I\)-sets and a decomposition of continuity via idealization. (English) Zbl 1074.54507
Summary: We introduce the notions of \(Q_I\)-sets and strong \(B_I\)-sets. Then we investigate properties of strong \(B_I\)-sets. Additionally, we obtain a new decomposition of continuity via idealization by using strong \(B_I\)-sets. Consequently, we extend a decomposition theorem of J. Dontchev [Acta Math. Hung. 75, 259–265 (1997; Zbl 0880.54014)] in terms of ideals.
MSC:
| 54C08 | Weak and generalized continuity |
| 54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |
| 54A05 | Topological spaces and generalizations (closure spaces, etc.) |
| 54C10 | Special maps on topological spaces (open, closed, perfect, etc.) |
