Torusüsteeme

Torusüsteeme, also known as torus systems, are a concept in topology and mathematics that describes objects resembling a doughnut or inner tube. A torus is formally defined as the product of two circles, S¹ × S¹, which can be visualized by taking a disk and identifying opposite edges in a specific way. This identification process creates a surface with a hole in the middle. Common examples include the surface of a donut, a bagel, or an inner tube for a tire.

The genus of a torus is one, meaning it has one "hole." This distinguishes it from simpler surfaces like a sphere (genus zero) or more complex surfaces with multiple holes. Torus systems can exist in higher dimensions, where a 2-torus is the standard doughnut shape, a 3-torus is formed by the product of three circles, and so on. These higher-dimensional tori have applications in various fields of physics, including string theory and cosmology, where they can represent compactified extra dimensions. The mathematical study of torus systems involves understanding their geometric properties, such as curvature, and their topological invariants, which remain unchanged under continuous deformations.