Point sets {interval, topology} can connect. Neighborhoods are open intervals. Unbounded intervals have no upper, no lower, or no upper or lower bound.
Open sets around points {accumulation point, topology} contain sequence points.
Functions can have all points inside n-sphere {bounded interval}.
Functions can be in closed and bounded intervals {compactness, topology}|. Intervals can have limits for all infinite subsets. Non-compact manifolds have edges or are infinite.
Curves, surfaces, spaces, or functions can have no breaks or missing values over real-number intervals {completeness, topology}|.
Curves, surfaces, spaces, or functions can have no breaks or missing values over real-number intervals {connectedness, topology}|. All convex figures connect. Interval boundaries are in two disjoint subsets. Intersections are never empty.
All points can have neighborhoods {continuous, topology}. Functions have inverses.
Curves, surfaces, spaces, or functions can be in closed intervals and have connectedness {continuum, topology}. Curves are one-dimensional continuums, closed at infinity. Sphere surfaces are two-dimensional continuums.
Two sets {disjoint set, topology} can share no points. Two disjoint open sets have disjoint closed sets inside {normal space}.
Points can be in sphere-like regions {neighborhood}|. Neighborhoods are open sets.
At curve or surface points, circles {circle of curvature} {osculating circle} can have radius equal to curvature radius.
Intervals {closed interval, topology} can have all points within or on higher boundary {upper bound, interval} and within or on lower boundary {lower bound, interval}.
Intervals {open interval, topology} can have all points within highest value {least upper bound, interval} and within lowest value {greatest lower bound, interval}. Neighborhoods are open intervals.
Outline of Knowledge Database Home Page
Description of Outline of Knowledge Database
Date Modified: 2022.0225