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

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

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 ...

The study of definable sets and functions in polish spaces.

A bridge of a connected graph is a graph edge whose removal disconnects the graph (Chartrand 1985, p. 45; Skiena 1990, p. 177). More generally, a bridge is an edge of a ...

Cut a sphere by a plane in such a way that the volumes of the spherical segments have a given ratio.

A clear-cut way of describing every object in a class in a one-to-one manner.