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The position of each piece also makes a significant difference: pawns near the edges are worth less than those near the centre, pawns close to promotion are worth far more, [1] pieces controlling the centre are worth more than average, trapped pieces (such as bad bishops) are worth less, etc.
In mathematics, a subset C of a real or complex vector space is said to be absolutely convex or disked if it is convex and balanced (some people use the term "circled" instead of "balanced"), in which case it is called a disk. The disked hull or the absolute convex hull of a set is the intersection of all disks containing that set.
A is a subset of B (denoted ) and, conversely, B is a superset of A (denoted ). In mathematics, a set A is a subset of a set B if all elements of A are also elements of B; B is then a superset of A. It is possible for A and B to be equal; if they are unequal, then A is a proper subset of B.
The interior of a closed subset of is a regular open subset of and likewise, the closure of an open subset of is a regular closed subset of . [2] The intersection (but not necessarily the union) of two regular open sets is a regular open set. Similarly, the union (but not necessarily the intersection) of two regular closed sets is a regular ...
In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set. [1] [2] In a topological space, a closed set can be defined as a set which contains all its limit points.
A subset S is both saturated and multiplicatively closed if and only if S is the complement of a union of prime ideals. [4] In particular, the complement of a prime ideal is both saturated and multiplicatively closed. The intersection of a family of multiplicative sets is a multiplicative set. The intersection of a family of saturated sets is ...