arXiv subjects

Victor Donjuán

Publications and source records attributed to Victor Donjuán.

2 recordsLinked to original sources

arXiv2021

Some notes on induced functions and group actions on hyperspaces

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 induced function in the case of the Fell and Attouch-Wets hyperspaces. Additionally we explore the problem of whether a continuous action of a topological group $G$ on a topological space $X$ induces a continuous action on $CL(X)$.

math.GN↗

arXiv2019

Separation axioms and covering dimension of asymmetric normed spaces

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 which states that every $T_1$ asymmetric normed space with compact closed unit ball must be finite-dimensional. We also explore the product structure of these spaces and characterize the topological (covering) dimension of all finite-dimensional asymmetric normed spaces.

math.GN↗