Quantum real projective spaces as quantum CW-complexes via topological graphs

We use the notion and properties of topological graphs to construct a quantum CW complex for quantum real projective spaces. This construction mirrors the CW complex construction in the classical case. Moreover, we introduce multipullback even-spheres as boundaries of noncommutative “cylinders” and show that they admit a gluing akin to the gluing of balls to the ends of a hollow closed cylinder.