The Cosmic Hausdorff Topology, the Bounded Hausdorff Topology and Continuity of Polarity

DOI10.2307/2048468zbMath0774.54008OpenAlexW4234196395MaRDI QIDQ3974474

Jean-Paul Penot

Publication date: 25 June 1992

Full work available at URL: https://doi.org/10.2307/2048468

zbMATH Keywords

polarityHausdorff distanceYoung-Fenchel correspondenceepi-distance topologybounded Hausdorff topologycosmic distance

Mathematics Subject Classification ID

Hyperspaces in general topology (54B20) Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) (54A20) Convex sets without dimension restrictions (aspects of convex geometry) (52A05)

Related Items

Well-posed optimization problems and a new topology for the closed subsets of a metric space, Stability of the geometric Ekeland variational principle: Convex case, Lipschitz behaviour of the Legendre-Fenchel transform, Wijsman convergence: A survey, Miscellaneous incidences of convergence theories in optimization and nonlinear analysis. I: Behavior of solutions, A splitting property of the upper bounded-Hausdorff convergence, On the Fell topology, More on the behaviors of fixed points sets of multifunctions and applications, Polar locally convex topologies and Attouch-Wets convergence, The Joly topology and the Mosco-Beer topology revisited, Quantitative stability analysis for maximal monotone operators and semi-groups of contractions, Topologies and convergences on the space of convex functions, The slice topology: a viable alternative to mosco convergence in nonreflexive spaces, Bornological convergence and shields, A metric approach to asymptotic analysis., Convergence of asymptotic directions, Persistence and stability of solutions of Hamilton-Jacobi equations, Efficiency and the uniform linear minorization of convex functions, A series of convex functions on a Banach space, On the convergence of subdifferentials of convex functions, A Characterization of Epi-Convergence in Terms of Convergence of Level Sets, Embeddings of bornological universes, Gap, excess and bornological convergence, Weak Topologies for the Closed Subsets of a Metrizable Space, Conditioning convex and nonconvex problems

Cites Work

• Unnamed Item
• Unnamed Item
• Another isometry for the Legendre-Fenchel transform
• Convergence of continuous linear functionals and their level sets
• Continuity of the Fenchel correspondence and continuity of polarities
• Convex analysis and measurable multifunctions
• Preservation of persistence and stability under intersections and operations. I: Persistence
• Une famille de topologies sur l'ensemble des fonctions convexes pour lesquelles la polarite est bicontinue
• Convergence of convex sets and of solutions of variational inequalities
• On the continuity of the Young-Fenchel transform
• Sur la fonction d'appui des ensembles convexes dans un espace localement convexe
• On the Young-Fenchel Transform for Convex Functions
• Isometries for the Legendre-Fenchel Transform
• A General Formula on the Conjugate of the Difference of Functions
• On Mosco convergence of convex sets
• On regularity conditions in mathematical programming
• The EPI-Distance Topology: Continuity and Stability Results with Applications to Convex Optimization Problems
• Conjugate Convex Functions and the Epi-Distance Topology
• Continuity of Some Convex-Cone-Valued Mappings
• Convex Analysis
• Operations on convergent families of sets and functions