Contraction Mapping Theorem: please explain complete metric space under operator and contraction

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Contraction Mapping Theorem:

For any metric space V that is complete (i.e. closed) under an operator T(v), where T is a γ-contraction, T converges to a unique fixed point and at a linear convergence rate of γ.

This is from field of artificial intelligence, called reinforcement learning, but I'm confused by some pure math terminology.

  1. I know that metric space being complete means that any Cauchy sequence converges, but what means that it's complete under operator?

  2. I read this on contraction in operator theory, is this correct interpretation of γ-contraction?