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A family of functors H_n(·) from the category of pairs of topological spaces and continuous maps, to the category of Abelian groups and group homomorphisms satisfies the ...

An axiom is a proposition regarded as self-evidently true without proof. The word "axiom" is a slightly archaic synonym for postulate. Compare conjecture or hypothesis, both ...

The five of Hilbert's axioms which concern geometric equivalence.

The eight of Hilbert's axioms which concern collinearity and intersection; they include the first four of Euclid's postulates.

The four of Hilbert's axioms which concern the arrangement of points.

The field axioms are generally written in additive and multiplicative pairs. name addition multiplication associativity (a+b)+c=a+(b+c) (ab)c=a(bc) commutativity a+b=b+a ...

Let Q_i denote anything subject to weighting by a normalized linear scheme of weights that sum to unity in a set W. The Kolmogorov axioms state that 1. For every Q_i in W, ...

The axioms formulated by Hausdorff (1919) for his concept of a topological space. These axioms describe the properties satisfied by subsets of elements x in a neighborhood ...

Given an event E in a sample space S which is either finite with N elements or countably infinite with N=infty elements, then we can write S=( union _(i=1)^NE_i), and a ...

For any set theoretic formula f(x,t_1,t_2,...,t_n), In other words, for any formula and set A there is a subset of A consisting exactly of those elements which satisfy the ...