1995/01/01 by Barry Simon · 5 citations
Mathematics · #Advanced Topology and Set Theory #Advanced Banach Space Theory #Fixed Point Theorems Analysis
paper · doi:10.2307/2118629
openalex publication_date 1995/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/13
Introduction The Baire category theorem implies that the family, F , of dense sets G ffi in a fixed metric space, X , is a candidate for generic sets since it is closed under countable intersections; and if X is perfect (has no isolated point), then A 2 F has uncountable intersections with any open ball in X . There is a long tradition of soft arguments to prove that certain surprising sets are generic. For example in C[0; 1], a generic function is nowhere differentiable. Closer to our concern here, Zamfirescu [20] has proven that a generic monotone function has purely singular continuous derivative, and Halmos [7]-Rohlin [14] have proven that a generic ergodic process is weak mixing but not mixing. We will say a set S ae X is Baire typical if it is a dense G ffi and a set