
## 4. Nuclearity

1. #### Problem 4.1.

Is every stably finite nuclear separable C*-algebra locally approximable by type I C*-algebras?
•     All presently known nuclear C*-algebras are obtained from $\mathbb C$ by taking closure under simple operations such as tensoring with finite-dimensional matrix algebras and taking inductive limits. They belong to the so-called bootstrap class.

#### Problem 4.2.

Does every nuclear C*-algebra belong to the bootstrap class?
• #### Problem 4.3.

Do all nuclear C*-algebras satisfy the UCT (Universal Coefficient Theorem)?

Cite this as: AimPL: Set theory and C* algebras, available at http://aimpl.org/settheorycstar.