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In mathematics, particularly in order theory, an upper bound or majorant [1] of a subset S of some preordered set (K, ≤) is an element of K that is greater than or equal to every element of S. [2] [3] Dually, a lower bound or minorant of S is defined to be an element of K that is less than or equal to every element of S.
The asymptotic property defines an equivalence relation on the set of geodesic rays, and the set of equivalence classes is called the ideal boundary ∂X of X. An equivalence class of geodesic rays is called a boundary point of X. For any equivalence class of rays and any point p in X, there is a unique ray in the class that issues from p. [1]
The boundary of a set in topology. The boundary operator on a chain complex in homological algebra. The boundary operator of a differential graded algebra. The conjugate of the Dolbeault operator on complex differential forms. The boundary ∂(S) of a set of vertices S in a graph is the set of edges leaving S, which defines a cut.
A class (), whose elements are called morphisms or maps or arrows. Each morphism f {\displaystyle f} has a source object a {\displaystyle a} and target object b {\displaystyle b} . The expression f : a ↦ b {\displaystyle f:a\mapsto b} would be verbally stated as " f {\displaystyle f} is a morphism from a to b ".
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially (that is, when the groups in question are realized as geometric symmetries or ...
Otsu's method is related to Fisher's linear discriminant, and was created to binarize the histogram of pixels in a grayscale image by optimally picking the black/white threshold that minimizes intra-class variance and maximizes inter-class variance within/between grayscales assigned to black and white pixel classes.
The term mapping class group has a flexible usage. Most often it is used in the context of a manifold M. The mapping class group of M is interpreted as the group of isotopy classes of automorphisms of M. So if M is a topological manifold, the mapping class group is the group of isotopy classes of homeomorphisms of M.
Division of Mathematical Sciences at the National Science Foundation, including a list of disciplinary areas supported; Faculty of Mathematical Sciences at University of Khartoum, offers academic degrees in Mathematics, Computer Sciences and Statistics; Programs of the Mathematical Sciences Research Institute