Integrating Graph Generalised Topological Spaces for Sustainable Development Modelling

Generalised Topological Spaces (GTS) provide greater flexibility in modelling real-world systems characterised by vague boundaries and incomplete information. The integration of graph theory through Graph Generalised Topological Spaces (GGTS) further enhances this framework by capturing the relational structures and intricate interdependencies inherent in sustainability challenges. This paper examines how GTS and GGTS can serve as powerful mathematical tools for understanding and addressing the complex challenges of sustainable development. We present the core ideas of GTS and GGTS—such as generalised and quasi-topologies, hereditary classes, and operators including interior, closure, and dense sets—and relate them to real-world systems. Using the United Nations’ 2030 Agenda and its 17 Sustainable Development Goals (SDGs) as context, we show how these frameworks naturally model uncertainty, incomplete data, and blurred boundaries that commonly arise in sustainability problems. Applications in areas such as resource networks, urban systems, and environmental planning illustrate how GTS and GGTS provide flexible and intuitive representations, offering insights where traditional mathematical models are often too rigid. Future research will focus on developing specific algorithms and computational tools based on these topological concepts to provide actionable insights for achieving the United Nations' Sustainable Development Goals.