About: Nowhere continuous function

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In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. If f is a function from real numbers to real numbers, then f is nowhere continuous if for each point x there is an ε > 0 such that for each δ > 0 we can find a point y such that 0 < |x − y| < δ and |f(x) − f(y)| ≥ ε. Therefore, no matter how close we get to any fixed point, there are even closer points at which the function takes not-nearby values.

Attributes	Values
rdf:type	disease
rdfs:label	Nowhere continuous function (en)
rdfs:comment	In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. If f is a function from real numbers to real numbers, then f is nowhere continuous if for each point x there is an ε > 0 such that for each δ > 0 we can find a point y such that 0 < \|x − y\| < δ and \|f(x) − f(y)\| ≥ ε. Therefore, no matter how close we get to any fixed point, there are even closer points at which the function takes not-nearby values. (en)
sameAs	Nowhere continuous function Nowhere continuous function
dbp:wikiPageUsesTemplate	dbt:Main_article dbt:More_citations_needed dbt:Short_description dbt:Snd dbt:Webarchive dbt:Abs dbt:Springer
Subject	Topology Types of functions Mathematical analysis
gold:hypernym	Function
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Nowhere_continuous_function?oldid=1072305251&ns=0
Wikipage page ID	333677 (xsd:integer)
page length (characters) of wiki page	3646 (xsd:nonNegativeInteger)
Wikipage revision ID	1072305251 (xsd:integer)
Link from a Wikipage to another Wikipage	Absolute value Blumberg theorem Topology Types of functions Mathematical analysis Dirichlet function Domain of a function Metric space Peter Gustav Lejeune Dirichlet Wolfram Demonstrations Project Hyperreal number Codomain Continuous function Function (mathematics) Indicator function Infinitesimal Weierstrass function Topological space Mathematics Rational number Real number Thomae's function
has abstract	In mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. If f is a function from real numbers to real numbers, then f is nowhere continuous if for each point x there is an ε > 0 such that for each δ > 0 we can find a point y such that 0 < \|x − y\| < δ and \|f(x) − f(y)\| ≥ ε. Therefore, no matter how close we get to any fixed point, there are even closer points at which the function takes not-nearby values. More general definitions of this kind of function can be obtained, by replacing the absolute value by the distance function in a metric space, or by using the definition of continuity in a topological space. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Nowhere_continuous_function
is Wikipage redirect of	Everywhere discontinuous function Everywhere discontinuous Nowhere continuous
is Link from a Wikipage to another Wikipage of	List of types of functions Baire function Blumberg theorem Bounded function Dirichlet function Discontinuous linear map Classification of discontinuities List of mathematical functions List of real analysis topics Darboux's theorem (analysis) Everywhere discontinuous function Lebesgue integration Numerical analysis Everywhere discontinuous Nowhere continuous

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