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A map f from a metric space M=(M,d) to a metric space N=(N,rho) is said to be uniformly continuous if for every epsilon>0, there exists a delta>0 such that ...

A theory which satisfies all the Eilenberg-Steenrod axioms with the possible exception of the long exact sequence of a pair axiom, as well as a certain additional continuity ...

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

The branch of mathematics which does not involve infinite sets, limits, or continuity.

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.

All elementary functions can be extended to the complex plane. Such definitions agree with the real definitions on the x-axis and constitute an analytic continuation.

A loose term for a true statement which may be a postulate, theorem, etc.

Archimedes' axiom, also known as the continuity axiom or Archimedes' lemma, survives in the writings of Eudoxus (Boyer and Merzbach 1991), but the term was first coined by ...

Cauchy's functional equation is the equation f(x+y)=f(x)+f(y). It was proved by Cauchy in 1821 that the only continuous solutions of this functional equation from R into R ...