Around Discontinuity for the Riesz Projection in the Uniform Metric

The present paper is based on a lecture given by the author at the conference ‘‘Complex Analysis and Related Problems’’ (Kazan, Russia, June 29–July 4, 2022). The lecture was devoted to the Glicksberg conjecture and a related but independent assertion that the sums of certain ideals in a uniform algebra are never closed. The present paper puts forward several new formulations in comparison with those given in the lecture and in the existing literature.