The concept of a "smallest unit of space" is a topic of active research and debate in theoretical physics. At present, our understanding of the fundamental structure of space is described by classical and quantum theories, such as general relativity and quantum mechanics, respectively. However, these theories do not provide a definitive answer to whether there exists a smallest unit of space.
In classical physics, space is considered continuous and infinitely divisible, allowing for arbitrarily small subdivisions. General relativity, which describes gravity and the curvature of spacetime, is formulated within a smooth manifold framework, assuming a continuous spacetime structure.
On the other hand, quantum mechanics introduces the concept of quantization, which suggests that certain physical quantities can only take discrete values. This idea is most apparent in the quantization of energy levels in atoms, for example. However, when it comes to space itself, the situation is less clear. Quantum field theory, which combines quantum mechanics with special relativity, treats particles and fields within a continuous spacetime framework.
The search for a theory of quantum gravity, which aims to reconcile general relativity with quantum mechanics, may shed light on the nature of space at the smallest scales. Theoretical frameworks such as string theory, loop quantum gravity, and other approaches propose the existence of fundamental entities or structures that could give rise to a discrete or granular structure of spacetime at extremely tiny scales. These theories suggest the possibility of a minimal length or a fundamental unit of space, sometimes referred to as the "Planck length" (about 1.6 x 10^-35 meters).
However, it is important to note that the existence of a smallest unit of space and the nature of spacetime at such scales are still highly speculative and remain an active area of research. Experimental verification and observational evidence to support or refute these ideas are currently beyond our technological capabilities.