Amin Talabeigi - Department of Mathematics, Payame Noor University, P.O. Box, ۱۹۳۹۵-۳۶۹۷, Tehran, Iran.

In this paper we intend to extract some types of generalized topologies from a topological space. To do this, we first generalize the derived set operator and the closure operator of a topological space using a class of subsets of the space, this collection is called the hereditary family since it is closed under the operation subset. The generalized closure operator induces a structure that is our desired generalized topology.

Generalized topology, Generalized topological space, Generalized derived set operator, Generalized closure operator. Hereditary family