definition of a limit. In topology, a function is continuous if it keeps "near" points "near." If two points are close together in the starting space, their images will stay relatively close in the destination space.
If we look at it through the lens of "nearness," topology becomes the study of . In standard geometry, we say two points are near if the distance between them is small (e.g., 0.01 mm). In topology, "nearness" is defined by neighborhoods . A point is near a set if every neighborhood of that point contains at least one piece of that set. definition of a limit
Topology has numerous real-world applications, including: definition of a limit. In topology