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Hilbert's problems are a set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total appearing in the printed address, ten were actually ...

Homology is a concept that is used in many branches of algebra and topology. Historically, the term "homology" was first used in a topological sense by Poincaré. To him, it ...

Let A and B be any sets with empty intersection, and let |X| denote the cardinal number of a set X. Then |A|+|B|=|A union B| (Ciesielski 1997, p. 68; Dauben 1990, p. 173; ...

A Dedekind ring is a commutative ring in which the following hold. 1. It is a Noetherian ring and a integral domain. 2. It is the set of algebraic integers in its field of ...

A stationary point process X is said to drive a model of continuum percolation theory if one of the characterizing axioms of the model hinges on the existence of X. In this ...

Fano's geometry is a finite geometry attributed to Fano from around the year 1892. This geometry comes with five axioms, namely: 1. There exists at least one line. 2. Every ...

Five point geometry is a finite geometry subject to the following three axioms: 1. there exist exactly five points, 2. each two distinct points have exactly one line on both ...

If T is a set of axioms in a first-order language, and a statement p holds for any structure M satisfying T, then p can be formally deduced from T in some appropriately ...

Suppose that G is a pseudograph, E is the edge set of G, and C is the family of edge sets of graph cycles of G. Then C obeys the axioms for the circuits of a matroid, and ...

According to many authors (e.g., Kelley 1955, p. 112; Joshi 1983, p. 162; Willard 1970, p. 99) a normal space is a topological space in which for any two disjoint closed sets ...