| dbo:abstract |
In topology, a formal ball is an extension of the notion of ball to allow unbounded and negative radius. The concept of formal ball was introduced by Weihrauch and Schreiber in 1981 and the negative radius case (the generalized formal ball) by Tsuiki and Hattori in 2008. Specifically, if is a metric space and the nonnegative real numbers, then an element of is a formal ball. Elements of are known as generalized formal balls. Formal balls possess a partial order defined by if , identical to that defined by set inclusion. Generalized formal balls are interesting because this partial order works just as well for as for , even though a generalized formal ball with negative radius does not correspond to a subset of . Formal balls possess the Lawson topology and the . (en) 形式球是一個拓樸學上的概念，將球體的概念繼續延伸至包括為負數的「球體」及不被包圍的狀況。形式球這個概念由Weihrauch & Schreiber (1981)提出，然後再由Tsuiki & Hattori (2008)一般化至包括球心距為負數（即一般化的形式球）的個案。 具體來說，如果是一個度量空間，以表示非負實數，則的元素就是在空間內的一個形式球。的元素則被稱為「一般化的形式球」。 (zh) |
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43092207 (xsd:integer) |
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1768 (xsd:nonNegativeInteger) |
| dbo:wikiPageRevisionID |
978652544 (xsd:integer) |
| dbo:wikiPageWikiLink |
dbr:Ball_(mathematics) dbr:Topology dbr:Lawson_topology dbc:Topology dbr:Metric_space dbr:Martin_topology |
| dbp:wikiPageUsesTemplate |
dbt:About dbt:Short_description |
| dct:subject |
dbc:Topology |
| rdfs:comment |
形式球是一個拓樸學上的概念，將球體的概念繼續延伸至包括為負數的「球體」及不被包圍的狀況。形式球這個概念由Weihrauch & Schreiber (1981)提出，然後再由Tsuiki & Hattori (2008)一般化至包括球心距為負數（即一般化的形式球）的個案。 具體來說，如果是一個度量空間，以表示非負實數，則的元素就是在空間內的一個形式球。的元素則被稱為「一般化的形式球」。 (zh) In topology, a formal ball is an extension of the notion of ball to allow unbounded and negative radius. The concept of formal ball was introduced by Weihrauch and Schreiber in 1981 and the negative radius case (the generalized formal ball) by Tsuiki and Hattori in 2008. Specifically, if is a metric space and the nonnegative real numbers, then an element of is a formal ball. Elements of are known as generalized formal balls. Formal balls possess a partial order defined by if , identical to that defined by set inclusion. Formal balls possess the Lawson topology and the . (en) |
| rdfs:label |
Formal ball (en) 形式球 (zh) |
| owl:sameAs |
freebase:Formal ball wikidata:Formal ball dbpedia-zh:Formal ball https://global.dbpedia.org/id/kZUX |
| prov:wasDerivedFrom |
wikipedia-en:Formal_ball?oldid=978652544&ns=0 |
| foaf:isPrimaryTopicOf |
wikipedia-en:Formal_ball |
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dbr:Ball_(mathematics) dbr:Lawson_topology |
| is foaf:primaryTopic of |
wikipedia-en:Formal_ball |