Siboid Proximity Spaces

Proximity theory is a branch of topology with numerous applications. Since its inception [V. A. E. Efremovič, The geometry of proximity. i, Matematicheskii Sbornik 73(1) (1952) 189–200] in the first half of the 20th century, proximity theory and its various generalizations have attracted the attention of researchers across diverse fields. This paper introduces, for the first time, a new generalized concept in proximity theory, referred to as the siboid proximity space. It represents a hybrid structure that combines the siboid proximity relation with the concept of a siboid space. In this paper, we present several fundamental results by introducing key concepts, including the siboid proximity relation, point-siboid proximity operator, siboid Hausdorff space, siboid regular space, and siboid normal space. As an application of the theoretical findings in artificial intelligence, it is demonstrated that a siboid motion vector field in the polar complex plane is governed by the structure of a siboid proximity space under a suitably defined siboid proximity relation and siboid space.