Models of topological geometry as a trend for creativity and innovation in the design process

With the growth of science and technology, along with the rise of the digital revolution andfuture sciences, new design trends have emerged based on fresh ideas about form and content. De-signers cannot achieve this with traditional methods. The challenge lies in research that overlooksinvestment in modern technologies to improve the design process, which aims at creativity andinnovation. Overall, this research seeks to elevate the field of topology, a part of pure mathemat-ics, as a new trend in digital design. It aims to clarify its features and explore its potential forcreative and innovative effects on the design process, developing it for future needs. Additionally,the research looks for a creative link between Topology and the design process. The purpose ofthis project is to understand the principles related to design philosophy of topology, which influ-ence interior space in terms of form and function. This approach will create a modern processto develop both interior and exterior architecture simultaneously. The importance of topologicalgeometry lies in its ability to foster new and creative thinking that enriches the design process andintroduces ideas for a different reality. This reality is a kinetic, changing, unpredictable space thatseeks to evolve. Finally, this research examines the origins and concept of topology and its visualaspects in design, using case studies to show how a topological approach can inspire creativity andinnovation in the design process.