Urysohn Spaces

Urysohn spaces are a type of mathematical structure in topology, a branch studying spaces and their properties. In a Urysohn space, for any two distinct points, it's possible to find neighborhoods around each that do not overlap, and additionally, these neighborhoods can be separated by a continuous function that maps the entire space into the interval [0,1], assigning 0 to one point and 1 to the other. This property ensures a high level of "separability," meaning points can be distinctly distinguished not just spatially but also via continuous functions, making Urysohn spaces important in understanding how spaces can be "separated" and analyzed.