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In literature there are the notions of generalized topology (in short GT) and hereditary class. Both these
notions have been studied extensively in different directions. Most of these studies evolved around considering a generalized topological space (in short GTS) endowed with certain hereditary class, and subsequently the nature of the resultant space is studied. By this, mathematicians intend to measure the quantum of deviations, the resultant space receives in respect of its basic properties. In our work we are deviating from this course of study. We consider an arbitrary GTS and certain collection of hereditary classes on this space and next we lift this collection to a GTS and the initial GTS will be embedded to this newly formulated space through certain well defined embedding map. Further we study the compactness property of this extension space. In course of this study we introduce certain notions and corresponding results for the theories of GTS as well as of hereditary class.
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