When an operator gives a unique generalized topology

Subject Areas : General topology

N. Sarkar ¹ , A. Das ² , T. E. Aman ³

1 - Department of Mathematics, Raiganj University, 733134, Raiganj, India
2 - Department of Mathematics, Raiganj University, 733134, Raiganj, India
3 - Department of Mathematics, Gangarampur College, 733124, Gangarampur, India

Received: 2023-04-13 Accepted : 2023-05-27 Published : 2023-06-01

Keywords: Generalized topology, $\mu$-interior, $\mu$-derived set, $\mu$-exterior, $\mu$-boundary,

Abstract :

In topology, we found enough literature on topological operators but in generalized topology, there is only $\mu$-interior, $\mu$-closure, and $\mu$-boundary operator. In this article, we explore different types of operators like $\mu$-derived set operator, $\mu$-exterior operator, $\mu$-preboundary operator in generalized topology. We have shown that any operator can be developed as the above operators impose certain conditions, giving a unique generalized topology in each case.

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