Interval-valued topological spaces associated with Λ_rg-closed sets

Abstract

In this paper, a new class of sets, called interval-valued Λ-regular generalized closed sets, is introduced in interval-valued topological spaces. The basic definitions and fundamental properties of these sets are investigated in detail. The corresponding interval-valued Λ-regular generalized open sets are also defined and studied. Furthermore, several relationships between these newly introduced sets and the existing classes of interval-valued closed and open sets are established. It is shown that interval-valued Λ-regular generalized closed sets constitute a weaker class than interval-valued closed sets. Similarly, interval-valued Λ-regular generalized open sets form a weaker class than interval-valued open sets. Appropriate examples are provided to illustrate and support the obtained results. This study extends the theory of generalized sets in interval-valued topological spaces and contributes to the further development of interval-valued topology.

1. Introduction

In 2026, I. Rajasekaran et al. [4] introduced the concept of interval-valued Λ_r-sets in interval-valued topological spaces. They also defined interval-valued λ_r-closed sets and interval-valued λ_r-open sets and investigated some of their basic properties. These concepts extended several classical notions in interval-valued topology and provided a broader framework for further study. Motivated by these developments, in this paper we introduce a new class of sets called interval-valued Λ-rg-closed sets and interval-valued Λ-rg-open sets in interval-valued topological spaces. Various fundamental properties and characterizations of these newly defined sets are studied in detail. Relationships between these sets and existing interval-valued closed and interval-valued open sets are also obtained. It is shown that interval-valued Λ-rg-closed sets and interval-valued Λ-rg-open sets are weaker forms of interval-valued closed sets and interval-valued open sets, respectively. These results contribute to the development of generalized structures in interval-valued topology.

This page shows an excerpt of the introduction. The full text, including the theorems, proofs and examples, is available in the PDF.

References

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Cite this article

Rajasekaran, I. & Nisha, P.S. (2026). Interval-valued topological spaces associated with Λ_rg-closed sets. Asia Mathematika, 10(2), 1–17. https://doi.org/10.5281/zenodo.23086265

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