We introduce a definition of $${\pi}$$ π being injective with respect to a generalized topology and a hereditary class where $${\pi}$$ π is a generalized quotient map between generalized topological spaces. This definition is mainly a sufficient condition to show several relations about a generalized topology and its induced generalized quotient topology when either is extended by a hereditary class or it can be regarded as an extension of a generalized topology via a hereditary class.

中文翻译：

---

广义商拓扑和遗传类

我们引入了 $${\pi}$$ π 是关于广义拓扑和遗传类的单射定义，其中 $${\pi}$$ π 是广义拓扑空间之间的广义商映射。这个定义主要是一个充分条件，表明当一个广义拓扑被一个遗传类扩展或者可以看作是一个广义拓扑通过一个遗传类的扩展时，关于广义拓扑及其诱导的广义商拓扑的几个关系。