Exploring generalized h-open sets
Ennis Rosasennisrafael@gmail.comDepartment of Natural and Exact Sciences Universidad de la CostaDepartment of Natural and Exact Sciences University of the CoastBarranquilla, 080001, Colombia0000-0001-8123-9344View full profile → , *Margot Salas-BrownCorresponding authormargot.salas@usa.edu.coDepartment of Mathematics Universidad de los AndesPrograma de Matemáticas Escuela de Ciencias Exactas e Ingeniería Universidad Sergio ArboledaBogotá, 11021, Colombiahttps://orcid.org/0000-0001-7202-8916View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Aug 2024
- Published Online:
- 11 Mar 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2185
- Pages:
- 2089–2096
Abstract
This work introduces a new class of sets, called h-open sets, defined through an operator γ and denoted by hγ-open sets, within the framework of a topological structure. The analysis focuses on the connection between these sets and those defined as γ-open, identifying precise criteria under which both families coincide. We also investigate properties of hγ-open sets, such as stability under unrestricted set unions and intersections involving only a limited number of components. Furthermore, we explore the connections between various notions of γ-open sets and h-open sets. Finally, we revisit a lemma from the literature that attempts to characterize h-open sets and provide counterexamples, as well as identify specific conditions under which the lemma holds true.
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References
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