Currently, Hubble's law is often considered as the observational evidence of an expanding universe. It is shown that Hubble's Law need not be related to the notion of Doppler redshifts of the light from receding Galaxies. In the derivation of the receding velocity, an implicit assumption, which implies no expansion, must be used. Moreover, the notion of receding velocity is incompatible with the local light speeds used in deriving the light bending. The notion of an expanding universe is based on an unverified assumption that a local distance in a physical space is similar to that of a mathematical Riemannian space embedded in a higher dimensional flat space, and thus the physical meaning of coordinates would necessarily depend on the metric. However, this assumption has been proven as theoretically invalid. In fact, a physical space necessarily has a frame of reference, which has a Euclidean-like structure that is independent of the yet to be determined physical metric and thus cannot be such an embedded space. In conclusion, the notion of an expanding universe could be just a mathematical illusion. 1 Introduction
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