Let $X$ be a Banach space. By Banach-Alaoglu and Krein-Milman Theorems, one can show that if $X$ is a dual space, then $X$ must have at least one extreme point of the closed unit ball. I am interested in its converse. More precisely, Question: Let $X$ be a Banach space. If the closed uni...

The title is the first sentence of Hermann Weyl's 1930 essay, "Levels of Infinity." He focuses on "the distinction between actuality and potentiality, between Being and Possibility." He opines "the impossibility of grasping the continuum as a fixed being," and concludes his essay w...