  We exhibit a new approach to the proofs of the existence of a large family of
almost isometric ideals in nonseparable Banach spaces and existence of a large
family of almost isometric local retracts in metric spaces. Our approach also
implies the existence of a large family of nontrivial projections on every dual
of a nonseparable Banach space. We prove three possible formulations of our
results are equivalent. Some applications are mentioned which witness the
usefulness of our novel approach.

Functional Analysis