Journal of Advanced Mathematical Modeling

Journal of Advanced Mathematical Modeling

A new type of the generalized interior and closure operators via hereditary classes

Document Type : Original Paper

Authors
Amin Talabeigi 1
Ghasem Mirhosseinkhani 2
1 Department of Mathematics, Payame Noor University
2 Sirjan University of technology
10.22055/jamm.2026.50643.2413
Abstract
In this paper, we intend to introduce and study an useful and practical example of the generalized
pr-derived-set and the generalized pre-co-derived-set operators under the name H-pre-closure and
H-pre-interior operator by using a hereditary class on a topological space. Finally, using these operator,
we introduce two operators H-closure and H-interior and show that all these operators induce a identical
generalized topology on a topological space. As a consequence, many results of topological operators
are generalized, clarified and stated via hereditary classes.
Keywords
Hereditary class
generalized topology
pre-interior operator
pre-closure operator
Subjects
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  • Receive Date 16 September 2025
  • Revise Date 19 December 2025
  • Accept Date 08 May 2026