A drop theorem without vector topology
An extension to bornological spaces is given for the 1972 drop theorem due to \textit{J.\,Danes} [Boll.\ Unione Mat.\ Ital., IV.\,Ser.\ 6, 369--375 (1972; Zbl 0236.47053)]; it includes the related statement in [\textit{J.--H.\thinspace Qiu}, J.~Math.\ Anal.\ Appl.\ 266, 288--297 (2002; Zbl 1004.46012)], expressed in a locally convex realm. As a byproduct of this, a corresponding version in such spaces is derived for Ekeland's variational principle and the Caristi--Kirk fixed point theorem.
scientific article; zbMATH DE number 5129659
scientific article