continuous in neighborhood of point

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• Continuous function — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia

• Continuous function (topology) — In topology and related areas of mathematics a continuous function is a morphism between topological spaces. Intuitively, this is a function f where a set of points near f(x) always contain the image of a set of points near x . For a general… …   Wikipedia

• Continuous mapping theorem — In probability theory, the continuous mapping theorem states that continuous functions are limit preserving even if their arguments are sequences of random variables. A continuous function, in Heine’s definition, is such a function that maps… …   Wikipedia

• continuous — adjective Etymology: Latin continuus, from continēre to hold together more at contain Date: 1673 1. marked by uninterrupted extension in space, time, or sequence 2. of a function having the property that the absolute value of the numerical …   New Collegiate Dictionary

• Saddle point — In mathematics, a saddle point is a point in the domain of a function of two variables which is a stationary point but not a local extremum. At such a point, in general, the surface resembles a saddle that curves up in one direction, and curves… …   Wikipedia

• Particular point topology — In mathematics, the particular point topology (or included point topology) is a topology where sets are considered open if they are empty or contain a particular, arbitrarily chosen, point of the topological space. Formally, let X be any set and… …   Wikipedia

• Degree of a continuous mapping — This article is about the term degree as used in algebraic topology. For other uses, see degree (mathematics). A degree two map of a sphere onto itself. In topology, the degree is a numerical invariant that describes a continuous mapping between… …   Wikipedia

• Potrero Point — San Francisco is the location of the earliest and most important industrial facilities in the Western United States on the eastern extension of San Francisco s Potrero Hill, a natural land mass extending into San Francisco Bay south of Mission… …   Wikipedia

• Misiurewicz point — A Misiurewicz point is a parameter in the Mandelbrot set (the parameter space of quadratic polynomials) for which the critical point is strictly preperiodic (i.e., it becomes periodic after finitely many iterations but is not periodic itself). By …   Wikipedia

• upper semi-continuous — adjective a) Such that, for each fixed number, the subspace of points whose images are at least that number is closed. b) Such that for each fixed point x there is some neighborhood whose images limit superior is x<nowiki/>s image …   Wiktionary

• Limit of a function — x 1 0.841471 0.1 0.998334 0.01 0.999983 Although the function (sin x)/x is not defined at zero, as x becomes closer and closer to zero, (sin x)/x becomes arbitrarily close to 1. It is said that the limit of (sin x)/x as x approache …   Wikipedia