Topology With Applications Topological | Spaces Via Near And Far

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.

Data is often messy and high-dimensional. TDA looks at the "shape" of data. By treating data points as a topological space, scientists can find "holes" in datasets that represent significant features. This is used in to identify different sub-types of tumors based on the connectivity of genetic expressions. 2. Robotics and Motion Planning If we look at it through the lens