Topology arises from mathematics and architecture in an inherent relationship that stems from their ancient intellectual concepts. Topology originated as a mathematical field and then spread to numerous sciences and arts, leading to contemporary architecture, relying on its theories as evidence of the comprehensiveness of this science and based on digital computing tools, modern technologies and advanced means of production. However, the features of this concept are still not common in the architectural field. Accordingly, the knowledge gap was identified as “the ambiguity of knowledge about the topological features of contemporary architectural products.”. The goal of the study is to develop, using an analytical descriptive approach, a comprehensive theoretical framework for the topological features represented by continuity, containment, and permeability. These characteristics were produced by significant topological theories that addressed this idea, such as Homotopy theory, Optimization theory, and Dimensional theory, whose concepts and vocabulary contributed to the development of a formative structure in modern architectural products. Then, using the descriptive-analytical technique, apply it to the chosen samples to generate a knowledge base that allows designers to express their originality, diversity, uniqueness, as well as inspiration. The results of the research showed the emergence of both of them the continuity feature represented by the clarity of the paths and the cancellation of the outage and the permeability feature through movement and spatial communication as the highest representation of the topology in the contemporary architectural products. While the conclusion was reached that topological theories contributed to supplying the structure of architectural products with several features that affected its contemporary formations and developed the ability to creative design.

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