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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
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.
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
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
Continuous modelling
Continuous modelling is the mathematical practice of applying a model to continuous data (data which has a potentially infinite number, and divisibility, of attributes). They often use differential equations and are converse to discrete modelling.
Modelling is generally broken down into several steps:
Making assumptions about the data: The modeller decides what is influencing the data and what can be safely ignored.
Making equations to fit the assumptions.
Solving the equations.
Verifying the results: Various statistical tests are applied to the data and the model and compared.
If the model passes the verification progress, putting it into practice.
If the model fails the verification progress, altering it and subjecting it again to verification; if it persists in fitting the data more poorly than a competing model, it is abandoned.