Resumen de Some examples concerning proximinality in Banach spaces

Zihou Zhang, Chunyan Liu, Yu Zhou

• We discuss the relationships between τ-strongly Chebyshev, τ-approximative compactness, τ-strong proximinality, and proximinality, where τ stands for the norm topology or weak topology. We consider four examples which illustrate the differences, and a counterexample that shows the question regarding the approximative n-compact Chebyshev subset, raised by Bandyopadhyay et al., is negative.