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In mathematics, a function is said to vanish at infinity if its values approach 0 as the input grows without bounds. There are two different ways to define this with one definition applying to functions defined on normed vector spaces and the other applying to functions defined on locally compact spaces. Aside from this difference, both of these notions correspond to the intuitive notion of adding a point at infinity, and requiring the values of the function to get arbitrarily close to zero as one approaches it. This definition can be formalized in many cases by adding an (actual) point at infinity.

Attributes	Values
rdfs:label	C0-Funktion (de) Vanish at infinity (en) 在無窮遠處消失 (zh)
rdfs:comment	In der Mathematik ist eine -Funktion eine stetige Funktion, die anschaulich betrachtet im Unendlichen verschwindet. Die Menge aller -Funktionen bildet einen normierten Raum. (de) In mathematics, a function is said to vanish at infinity if its values approach 0 as the input grows without bounds. There are two different ways to define this with one definition applying to functions defined on normed vector spaces and the other applying to functions defined on locally compact spaces. Aside from this difference, both of these notions correspond to the intuitive notion of adding a point at infinity, and requiring the values of the function to get arbitrarily close to zero as one approaches it. This definition can be formalized in many cases by adding an (actual) point at infinity. (en) 在數學中，若一個賦範向量空間上的函數滿足當時，則稱該函數在無窮遠處消失。例如，下面這個定義在實數線上的函數在無窮遠處消失。另一個例子是其中與為實數，且對應到上的這一個點。 (zh)
dcterms:subject	Mathematical analysis
Wikipage page ID	461986 (xsd:integer)
Wikipage revision ID	1083869630 (xsd:integer)
Link from a Wikipage to another Wikipage	Scalar multiplication Vector space Compact space Mathematical analysis Mathematics Edwin Hewitt Function (mathematics) Locally compact Smooth function Partial derivative Banach space Locally compact space Addition Collocation method Normed space Mathematical analysis Distribution (mathematics) Pointwise Positive number Real number Set (mathematics) Real line Normed vector space
sameAs	Schwartz space Schwartz space Schwartz space Schwartz space Schwartz space Schwartz space
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_book dbt:Em dbt:Main dbt:Mvar dbt:Reflist
has abstract	In der Mathematik ist eine -Funktion eine stetige Funktion, die anschaulich betrachtet im Unendlichen verschwindet. Die Menge aller -Funktionen bildet einen normierten Raum. (de) In mathematics, a function is said to vanish at infinity if its values approach 0 as the input grows without bounds. There are two different ways to define this with one definition applying to functions defined on normed vector spaces and the other applying to functions defined on locally compact spaces. Aside from this difference, both of these notions correspond to the intuitive notion of adding a point at infinity, and requiring the values of the function to get arbitrarily close to zero as one approaches it. This definition can be formalized in many cases by adding an (actual) point at infinity. (en) 在數學中，若一個賦範向量空間上的函數滿足當時，則稱該函數在無窮遠處消失。例如，下面這個定義在實數線上的函數在無窮遠處消失。另一個例子是其中與為實數，且對應到上的這一個點。 (zh)
prov:wasDerivedFrom	wikipedia-en:Vanish_at_infinity?oldid=1083869630&ns=0
page length (characters) of wiki page	4590 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Vanish_at_infinity
is Link from a Wikipage to another Wikipage of	Multiplier algebra Bound state List of mathematical jargon Riesz–Markov–Kakutani representation theorem Gelfand representation Continuous functions on a compact Hausdorff space Stone–Weierstrass theorem Feller process Fréchet algebra Locally compact space Banach algebra Support (mathematics) High harmonic generation Zero of a function Group Hopf algebra Riemann–Lebesgue lemma Vague topology Rapidly decreasing Rapidly decreasing function
is Wikipage redirect of	Rapidly decreasing Rapidly decreasing function
is foaf:primaryTopic of	wikipedia-en:Vanish_at_infinity

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