Fredholm operators and the wave-particle duality in Cantorian space

This note analyses the so called wave-particle dulaity from the point of view of the geometry and the topology of micro spacetime. It is shown that the so called index theorem of Toepliz operators is consistant with the irreducible spacial uncertainty of Cantorian spacetime and that this, in turn, is responsible for various paradoxial notions in quantum physics, such as the wave-particle duality.