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We exhibit a new approach to the proofs of the existence of a large family ofalmost isometric ideals in nonseparable Banach spaces and existence of a largefamily of almost isometric local retracts in metric spaces. Our approach alsoimplies the existence of a large family of nontrivial projections on every dualof a nonseparable Banach space. We prove three possible formulations of ourresults are equivalent. Some applications are mentioned which witness theusefulness of our novel approach.

Note on almost isometric ideals and local retracts in Banach and metric spaces