For 10 points, name this property of a function, defined by Cauchy in terms of two related infinitesimal changes, which is usually contingent on a function's graph having no "holes" or "jumps."
A functor F from categories C to D has this property if it commutes with limits; similarly, functors of this type preserve all small limits. The morphisms of the category Top are maps which all have this property. In descriptive set theory, this property is studied as the intersection between all the G-delta sets, which quantify oscillation as less than epsilon. According to one definition, this property is possessed by the Cantor function, and Peano curves have that property when the exponent is one-half. The Heine-Cantor theorem concerns this property between metric spaces M and N; when M is compact, (*) every function possessing this property must possess the uniform type of it. One set of functions can comply with the Hölder definition of this property but not the Lipschitz definition. That set of nowhere differentiable functions, along with an epsilon-delta definition of this property, is named for Weierstrass. For 10 points, name this property of a function, defined by Cauchy in terms of two related infinitesimal changes, which is usually contingent on a function's graph having no "holes" or "jumps."
A functor F from categories C to D has this property if it commutes with limits; similarly, functors of this type preserve all small limits.
continuous [accept word forms]