On Three Open Problems Related to Quasi Relative Interior

We give answers to two questions formulated by J. Borwein and R. Goebel [Notions of relative interior in Banach spaces, J. Math. Sci. (N. Y.) 115(4) (2003) 2542–2553] and to a conjecture formulated by S. M. Grad and E. L. Pop [Vector duality for convex vector optimization problems by means of the quasi-interior of the ordering cone, Optimization 63(1) (2014) 21–37] related to calculus rules for quasi (relative) interior.