41 citations · 41 across the 4 of their papers we have counts for
10 papers
Some notes on induced functions and group actions on hyperspaces
Victor Donjuán, Natalia Jonard-Pérez, Ananda López-Poo
We discuss the problem of when a continuous map between topological spaces induces a continuous function between their respective hyperspaces. We characterize the continuity of the…
A Jordan Curve Theorem for 2-dimensional Tilings
Diego Fajardo-Rojas, Natalia Jonard-Pérez
The classical Jordan curve theorem for digital curves asserts that the Jordan curve theorem remains valid in the Khalimsky plane. Since the Khalimsky plane is a quotient space of $…
Separation axioms and covering dimension of asymmetric normed spaces
Victor Donjuán, Natalia Jonard-Pérez
In this paper, we approach the question if some of the separation axioms are equivalent in the class of asymmetric normed spaces. In particular, we make a remark on a known theorem…
Local compactness in right bounded asymmetric normed spaces
Natalia Jonard-Pérez, Enrique A. Sánchez-Pérez
We characterize the finite dimensional asymmetric normed spaces which are right bounded and the relation of this property with the natural compactness properties of the unit ball,…
A short proof of Grünbaum's Conjecture about affine invariant points
Natalia Jonard-Pérez
Let us denote by the hyperspace of all convex bodies of equipped with the Hausdorff distance topology. An affine invariant point is a continuous an…
A pseudometric invariant under similarities in the hyperspace of non-degenerated compact convex sets of
Bernardo González Merino, Natalia Jonard-Pérez
In this work we define a new pseudometric in , the hyperspace of all non-degenerated compact convex sets of , which is invariant under similarities. We…
Extreme points and geometric aspects of compact convex sets in asymmetric normed spaces
Natalia Jonard-Pérez, Enrique A. Sánchez-Pérez
Inspired in the theorem of Krein-Milamn, we investigate the existence of extreme points in compact convex subsets of asymmetric normed spaces. We focus our attention in the finite…
Compact convex sets in 2-dimensional asymmetric normed lattices
Natalia Jonard-Pérez, Enrique A. Sánchez-Pérez
We study the geometric structure of compact convex sets in 2-dimensional asymmetric normed lattices. We prove that every q-compact convex set is strongly q-compact and we give a co…
Equivariant absolute extensor property on hyperspaces of convex sets
Natalia Jonard-Pérez
Let G be a compact group acting on a Banach space L by means of linear isometries. The action of G on L induces a natural continuous action on cc(L), the hyperspace of all compact…
Hyperspaces of convex bodies of constant width
Sergey Antonyan, Natalia Jonard-Pérez, Saúl Juárez-Ordóñez
Let n be a natural number equal or greater than 2. In this paper we study the topological structure of certain hyperspaces of convex subsets of constant width, equipped with the Ha…