As daily problems involve a great deal of data and ambiguity, it has become vital to build new mathematical ways cope with them, soft set theory is the greatest tool for doing so. result, we study methods generating topologies through several operators. A topology known be determined by system special sets, which are called open (dually closed) sets. The relationship between specific types thei...

Abstract A generating set for a finite group G is minimal if no proper subset generates , and $m(G)$ denotes the maximal size of . We prove conjecture Lucchini, Moscatiello Spiga by showing that there exist $a,b> 0$ such any satisfies $m(G) \leqslant \cdot \delta (G)^b$ $\delta (G) = \sum _{p \text { prime}} m(G_p)$ where $G_p$ Sylow p -subgroup To do this, we first bound all almost simple g...