• Amsterdam properties of Wijsman hyperspaces

      Cao, J; Junnila, HJK (American Mathematical Society, 2010)
      In this paper we show the following results: (i) there exists a separable metric space of the first category whose Wijsman hyperspace is almost countably subcompact; (ii) there exists a σ-discrete crowded metric space whose ...
    • Baire spaces and the Wijsman topology

      Cao, J; Tomita, A (AUT University, 2007)
      In 1960s, when he studied Banach space geometry, R. Wijsman considered the weak topology on the collection of nonempty closed subsets of a metric space generated by the distance functionals viewed as functions of set ...
    • Baire spaces and Vietoris hyperspaces

      Cao, J; Garcia Ferreira, S; Gutev, V (The American Mathematical Society, 2007)
      We prove that if the Vietoris hyperspace CL(X) of all nonempty closed subsets of a space X is Baire, then all finite powers of X must be Baire spaces. In particular, there exists a metrizable Baire space whose Vietoris ...
    • Baire spaces, Tychonoff powers and the Vietoris topology

      Cao, J; Tomita, AH (American Mathematical Society, 2007)
      In this paper, we show that if the Tychonoff power Xω of a quasiregular space X is Baire, then its Vietoris hyperspace 2X is also Baire. We also provide two examples to show (i) the converse of this result does not hold in ...
    • Bornologies and hyperspaces

      Cao, J (New Zealand Mathematical Society, 2011)
      A bornology on a nonempty set X is a family of subsets of X that is closed under taking finite unions, that is hereditary, and that forms a cover of X. Bornologies have been widely applied in functional analysis and topology ...
    • Games and Metrisability of Manifolds

      Cao, J; Gauld, DB; Greenwood, S; Mohamad, A (Joint committee of the New Zealand Mathematical Society and the Department of Mathematics of the University of Auckland., 2008)
      Using topological games we investigate connections between properties of topological spaces and their spaces of continuous functions with the compact-open topology. This leads to new criteria for metrisability of a manifold. ...
    • Infinite dimensional mixed economies with asymmetric information

      Bhowmik, A; Cao, J (Munich Personal RePEc Archive (MPRA), Munich University, 2011)
      In this paper, we study asymmetric information economies consisting of both non-negligible and negligible agents and having ordered Banach spaces as their commodity spaces. In answering a question of Hervés-Beloso and ...
    • On the core and Walrasian expectations equilibrium in infinite dimensional commodity spaces

      Bhowmik, A; Cao, J (Munich Personal RePEc Archive (MPRA), Munich University, 2011)
      In this paper, we establish two different characterizations of Walrasian expectations allocations by the veto power of the grand coalition in an asymmetric information economy having finitely many agents and states of ...
    • Oscillation Revisited

      Beer, G; Cao, J (arXiv, 2016)
      In previous work by Beer and Levi [8, 9], the authors studied the oscillation Ω(f, A) of a function f between metric spaces hX, di and hY, ρi at a nonempty subset A of X, defined so that when A = {x}, we get Ω(f, {x}) ...
    • Quasicontinuous selections of upper continuous set-valued mappings

      Cao, J; Moors, WB (Michigan State University Press, 2006)
      In this paper, we extend a theorem of Matejdes on quasicontinuous selections of upper Baire continuous set-valued mappings from compact (or separable) metric range spaces to regular T1 range spaces. In addition, we also ...
    • Robust portfolio selection problem for an insurer with exponential utility preference

      Zhao, H; Rong, X; Cao, J (World Scientific and Engineering Academy and Society, 2011)
      In this paper, we consider the robust portfolio selection problem for an insurer in the sense of maximizing the exponential utility of his wealth. This special robust investment problem, where underwriting results and a ...
    • The Baire property in hit-and-miss topologies

      Cao, J (AUT University, 2008)
      In the past ten years, there has been a great progress in determining when hyperspaces have the Baire property, and several problems have been solved. I this talk, I shall explore the Baire property of hyperspace equipped ...
    • The ideal generated by sigma-nowhere dense sets

      Cao, J; Greenwood, S (Applied General Topology, Universidad Politecnica de Valencia, 2006)
      In this paper, we consider the ideal I¾ generated by all ¾-nowhere dense sets in a topological space. Properties of this ideal and its relations with the Volterra property are explored. We show that I¾ is compatible with ...
    • The ideal generated by sigma-nowhere dense sets

      Cao, J; Greenwood, S (Universidad Politecnica de Valencia, 2006)
      In this paper, we consider the ideal I_σ generated by all σ-nowhere dense sets in a topological space. Properties of this ideal and its relations with the Volterra property are explored. We show that I_σ is compatible with ...
    • The Wijsman Convergence

      Cao, J (AUT University, 2010)
      In 1960's, when he studied some optimum properties of sequential probability ratio test, R. A. Wijsman considered a mode of convergence for sequences of closed sets such that if a sequence of proper lower semicontinuous ...
    • Three Open Problems on the Wijsman Topology

      Cao, J (arXiv, 2016)
      Since it first emerged in Wijsman's seminal work [29], the Wijsman topology has been intensively studied in the past 50 years. In particular, topological properties of Wijsman hyperspaces, relationships between the Wijsman ...
    • Volterra versus Baire spaces?

      Cao, J; Junnila, H (AUT University, 2006)
      A topological space X is called Volterra if for each pair of real-valued functions f,g: X → R such that C(f) and C(g) are dense, C(f)∩C(g) is also dense, where C(f) and C(g) are sets of points of continuity of f and g ...
    • Weak continuity properties of topologized groups

      Cao, J (AUT University, 2008)
      A topologized group is simply a group (G, ·) equipped with a topology t. The question as to when a topologized group (G, ·, t) is a topological group has been studied by many authors in the literature. In the recent work ...
    • When is a Volettera space Baire?

      Cao, J; Junnila, HJK (University of Patras, 2006)
      In this talk, we study the problem when a Volterra space is Baire. It is shown that every stratifiable Volterra space is Baire. This answers affirmatively a question of Gruenhage and Lutzer in 2000. Further, it is established ...
    • Wijsman convergence: topological properties and embeddings

      Cao, J (AUT University, 2010)
      In 1966, R. A. Wijsman studied some optimum properties of the sequential probability ratio test, he considered a mode of convergence for sequences of closed convex sets in R^n. Since then, this type of convergence has ...