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Gauge theory studies principal bundle connections, called gauge fields, on a principal bundle. These connections correspond to fields, in physics, such as an electromagnetic ...

Number Theory

A subset E of a topological space S is said to be nonmeager if E is of second category in S, i.e., if E cannot be written as the countable union of subsets which are nowhere ...

A member of a collection of sets is said to be maximal if it cannot be expanded to another member by addition of any element. Maximal sets are important in graph theory since ...

A subset A subset= X of a topological space X is said to be disconnected if it is not connected.

A subset S of a topological space X is compact if for every open cover of S there exists a finite subcover of S.

The theory of point sets and sequences having a uniform distribution. Uniform distribution theory is important in modeling and simulation, and especially in so-called Monte ...

Three sets of three lines such that each line is incident with two from both other sets.

If F is a sigma-algebra and A is a subset of X, then A is called measurable if A is a member of F. X need not have, a priori, a topological structure. Even if it does, there ...

Computational number theory is the branch of number theory concerned with finding and implementing efficient computer algorithms for solving various problems in number ...