Some examples in the non-stable K -theory of C*-algebras

We give a necessary and sufficient condition for lifting projections from the corona algebra of I = C( X) ⊗ [special characters omitted] to the multiplier algebra where X is [0, 1], [0, ∞), (–∞, ∞), or [special characters omitted]. Also, we give criteria for homotopy equivalence, unitary equivalence, and Murray-von Neumann equivalence of two projections in the corona algebra. In addition, we show some examples of other lifting problems: lifting unitaries to unitaries, lifting unitaries to extremal partial isometries, and lifting extremal partial isometries to extremal partial isometries