2022/01/17 by Silva, Bryant Rosado, Biezuner, Rodney Josué
#FOS: Mathematics #General Topology (math.GN)
paper · doi:10.48550/arxiv.2201.06369
When one considers the collection H(ℝn) of all compact subsets of ℝn and equip it with a topology, many questions can be asked about the topological space one ends up with. This is an example of a hyperspace, a mathematical object which has been studied in a more abstract setting since the beginning of the 20th century. Here we give an elementary proof of the path-connectedness of H(ℝn), with the topology induced by the Hausdoff metric, by exploring the vector structure of ℝn and using only basic ideas of topology of metric spaces that undergraduate students with just a basic knowledge of these concepts will be able to understand.