We characterize the $C^\star$-algebras for which openness of projections in their second duals is preserved under Murray-von Neumann equivalence. They are precisely extensions annihilator by commutative $C^\star$-algebras. also show that all open.

In [8, 9] M. G. Corrales Garcia, D. M. Barquero, C. Martin Gonzalez, M. Siles Molina, J. F Solanilla Hernandez described the center of a Leavitt path algebra and characterized it in terms of the underlying graph. We offer a different characterization of the center. In particular, we prove that the Boolean algebra of central idempotents of a Leavitt path algebra of a finite graph is isomorphic t...