In topology, the Denjoy–Riesz theorem states that every compact set of totally disconnected points in the Euclidean plane can be covered by a continuous image of the unit interval, without self-intersections (a Jordan arc). == Definitions and statement == A topological space is zero-dimensional according to the Lebesgue covering dimension if every finite open cover has a refinement that is also an open cover by disjoint sets.
In topology, the Denjoy–Riesz theorem states that every compact set of totally disconnected points in the Euclidean plane can be covered by a continuous image of the unit interval, without self-intersections (a Jordan arc). == Definitions and statement == A topological space is zero-dimensional according to the Lebesgue covering dimension if every finite open cover has a refinement that is also an open cover by disjoint sets.
Source: Wikipedia "Denjoy–Riesz theorem" · CC BY-SA 4.0
Share this article: X · Bluesky