Boundary (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S, not belonging to the interior of S. An element of the boundary of S is called a boundary point of S. Notations used for boundary of a set S include bd(S), fr(S), and ∂S. Some authors (for example Willard, in General Topology) use the term frontier, instead of boundary in an attempt to avoid confusion with the concept of boundary used in algebraic topology and manifold theory.
A connected component of the boundary of S is called a boundary component of S.
Read more about Boundary (topology): Common Definitions, Examples, Properties, Boundary of A Boundary
Famous quotes containing the word boundary:
“If you meet a sectary, or a hostile partisan, never recognize the dividing lines; but meet on what common ground remains,—if only that the sun shines, and the rain rains for both; the area will widen very fast, and ere you know it the boundary mountains, on which the eye had fastened, have melted into air.”
—Ralph Waldo Emerson (1803–1882)