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jointly continuous topology - translation to russian
WIKIMEDIA DISAMBIGUATION PAGE
Strongly continuous; Strong topology (disambiguation)
jointly continuous topology
совместно непрерывная топология
continuous extension
![The graph of a [[cubic function]] has no jumps or holes. The function is continuous.](https://commons.wikimedia.org/wiki/Special:FilePath/Brent method example.svg?width=200 "The graph of a [[cubic function]] has no jumps or holes. The function is continuous.")
![section 2.1.3]]).](https://commons.wikimedia.org/wiki/Special:FilePath/Discontinuity of the sign function at 0.svg?width=200 "section 2.1.3]]).")
![Riemann sphere]] is often used as a model to study functions like the example.](https://commons.wikimedia.org/wiki/Special:FilePath/Function-1 x.svg?width=200 "Riemann sphere]] is often used as a model to study 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.](https://commons.wikimedia.org/wiki/Special:FilePath/Homografia.svg?width=200 "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.")
![oscillation]].](https://commons.wikimedia.org/wiki/Special:FilePath/Rapid Oscillation.svg?width=200 "oscillation]].")
.svg?width=200 "Point plot of Thomae's function on the interval (0,1). The topmost point in the middle shows f(1/2) = 1/2.")
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
математика
непрерывное расширение
discontinuous function
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
общая лексика
разрывная функция
математика
прерывная функция
Definition
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)
Wikipedia
Strong topology
In mathematics, a strong topology is a topology which is stronger than some other "default" topology. This term is used to describe different topologies depending on context, and it may refer to:
- the final topology on the disjoint union
- the topology arising from a norm
- the strong operator topology
- the strong topology (polar topology), which subsumes all topologies above.
A topology τ is stronger than a topology σ (is a finer topology) if τ contains all the open sets of σ.
In algebraic geometry, it usually means the topology of an algebraic variety as complex manifold or subspace of complex projective space, as opposed to the Zariski topology (which is rarely even a Hausdorff space).
