Work

Submaximality, Connectedness, and δβI-Continuous Mappings in Ideal Spaces

Year: 2026

Type: article

Abstract: This paper extends the concepts of submaximality, connectedness, and hyperconnectedness to ideal topological spaces by means of δβI-open sets, which constitute a class of generalized open sets. Initially, we establish a collection of equivalent conditions that define the δβI-submaximality of an ideal topological space (T, τ, I). This study then discusses δβI-connectedness, which is a more general form of classical connectedness. We demonstrate that some mappings preserve this form of relationship. Finally, we introduce a generalization of hyperconnectedness based on δβI-open sets and provide characterizations of these spaces. These findings jointly augment the theory of ideal topological spaces by establishing coherent frameworks for submaximality, connectedness, and hyperconnectedness while expanding their applicability to more expansive topological situations where conventional separation axioms and continuity ideas are insufficient.

Source: Mathematics

DOI: 10.3390/math14142656

Authors: Chawalit Boonpok, Areeyuth Sama-Ae

Institutions: Mahasarakham University, Prince of Songkla University

Language: English

Topic: Advanced Topology and Set Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Prince of Songkla University