NationMaster - Encyclopedia: Cauchy space

In general topology, a Cauchy space is a structure introduced by H. H. Keller in 1968, as an axiomatic tool derived from the idea of a Cauchy filter, in order to study completeness in topological spaces. The category of Cauchy spaces and Cauchy continuous maps is cartesian closed, and contains the category of proximity spaces.

See also complete space.

Categories: Stub | General topology

Results from FactBites:

History of the Fundamental Theorem of Calculus (1146 words)
	Cauchy defined the integral of any continuous function on the interval [a,b] to be the limit of the sums of areas of thin rectangles.
	Cauchy proved the Mean Value Theorem for Integrals and used it to prove the Fundamental Theorem of Calculus for continuous functions, giving the form of the proof used today's calculus texts.
	Cauchy the first to define fully the ideas of convergence and absolute convergence of infinite series, including the development of the ratio and root tests for convergence of series.

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