continuous map - определение. Что такое continuous map
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Что (кто) такое continuous map - определение

FUNCTION SUCH THAT THE PREIMAGE OF AN OPEN SET IS OPEN
Continuity property; Continuous map; Continuous function (topology); Continuous (topology); Continuous mapping; Continuous functions; Continuous maps; Discontinuity set; Noncontinuous function; Discontinuous function; Continuity (topology); Continuous map (topology); Sequential continuity; Stepping Stone Theorem; Continuous binary relation; Continuous relation; Topological continuity; Right-continuous; Right continuous; Left continuous; Left-continuous; C^1; Continuous fctn; Cts fctn; E-d definition; Continuous variation; Continuity space; Continuous space; Real-valued continuous functions; Left-continuous function; Right-continuous function; Left- or right-continuous function; Continuity at a point; Continuous at a point; Continuous extension
  • The graph of a [[cubic function]] has no jumps or holes. The function is continuous.
  • 1=exp(0) = 1}}
  • section 2.1.3]]).
  • 1=''ε'' = 0.5}}.
  • Riemann sphere]] is often used as a model to study of functions like the example.
  • The graph of a continuous [[rational function]]. The function is not defined for <math>x = -2.</math> The vertical and horizontal lines are [[asymptote]]s.
  • For a Lipschitz continuous function, there is a double cone (shown in white) whose vertex can be translated along the graph, so that the graph always remains entirely outside the cone.
  • oscillation]].
  • The sinc and the cos functions
  • Point plot of Thomae's function on the interval (0,1). The topmost point in the middle shows f(1/2) = 1/2.
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Continuous function         
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as discontinuities.
continuous function         
A function f : D -> E, where D and E are cpos, is continuous if it is monotonic and f (lub Z) = lub f z | z in Z for all directed sets Z in D. In other words, the image of the lub is the lub of any directed image. All additive functions (functions which preserve all lubs) are continuous. A continuous function has a {least fixed point} if its domain has a least element, bottom (i.e. it is a cpo or a "pointed cpo" depending on your definition of a cpo). The least fixed point is fix f = lub f^n bottom | n = 0..infinity (1994-11-30)
Degree of a continuous mapping         
  • A degree two map of a [[sphere]] onto itself.
GENERALIZATION OF WINDING NUMBER
Degree (continuous map); Degree of a mapping; Degree of a map; Degree of a continuous map; Brouwer degree; Degrees of maps
In topology, the degree of a continuous mapping between two compact oriented manifolds of the same dimension is a number that represents the number of times that the domain manifold wraps around the range manifold under the mapping. The degree is always an integer, but may be positive or negative depending on the orientations.

Википедия

Continuous function

In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as discontinuities. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is not continuous. Up until the 19th century, mathematicians largely relied on intuitive notions of continuity, and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity.

Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are the most general continuous functions, and their definition is the basis of topology.

A stronger form of continuity is uniform continuity. In order theory, especially in domain theory, a related concept of continuity is Scott continuity.

As an example, the function H(t) denoting the height of a growing flower at time t would be considered continuous. In contrast, the function M(t) denoting the amount of money in a bank account at time t would be considered discontinuous, since it "jumps" at each point in time when money is deposited or withdrawn.