About: Subnet (mathematics)

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Subnet (mathematics) Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)
QRcode icon

http://dbpedia.demo.openlinksw.com/describe/?url=http%3A%2F%2Fdbpedia.org%2Fresource%2FSubnet_%28mathematics%29&invfp=IFP_OFF&sas=SAME_AS_OFF

In topology and related areas of mathematics, a subnet is a generalization of the concept of subsequence to the case of nets. The analogue of "subsequence" for nets is the notion of a "subnet". The definition is not completely straightforward, but is designed to allow as many theorems about subsequences to generalize to nets as possible. This article discusses the definition due to Stephen Willard (the other definitions are described in the article Filters in topology#Subnets).

Attributes	Values
rdf:type	Thing
rdfs:label	Subnet (mathematics) (en)
rdfs:comment	In topology and related areas of mathematics, a subnet is a generalization of the concept of subsequence to the case of nets. The analogue of "subsequence" for nets is the notion of a "subnet". The definition is not completely straightforward, but is designed to allow as many theorems about subsequences to generalize to nets as possible. This article discusses the definition due to Stephen Willard (the other definitions are described in the article Filters in topology#Subnets). (en)
rdfs:seeAlso	Topology Filters
dcterms:subject	Topology
Wikipage page ID	12687840 (xsd:integer)
Wikipage revision ID	1121219125 (xsd:integer)
Link from a Wikipage to another Wikipage	Compact space Mathematics Closure (topology) Function composition Stephen Willard Subsequence John L. Kelley Tychonoff plank 1970 Ceiling function Topology Topology Filters in topology Cardinality Directed set Cofinal (mathematics) Neighbourhood system Net (mathematics) Sequence Image (mathematics) Uncountable set Order-preserving Final function Cofinal subset Cluster point of a net Monotone function (order theory)
sameAs	Subnet (mathematics) Subnet (mathematics) Subnet (mathematics)
dbp:wikiPageUsesTemplate	dbt:Annotated_link dbt:Cite_book dbt:Em dbt:Reflist dbt:See_also dbt:Sfn dbt:Visible_anchor dbt:Schechter_Handbook_of_Analysis_and_Its_Foundations dbt:Willard_General_Topology
has abstract	In topology and related areas of mathematics, a subnet is a generalization of the concept of subsequence to the case of nets. The analogue of "subsequence" for nets is the notion of a "subnet". The definition is not completely straightforward, but is designed to allow as many theorems about subsequences to generalize to nets as possible. There are three non-equivalent definitions of "subnet". The first definition of a subnet was introduced by John L. Kelley in 1955 and later, Stephen Willard introduced his own (non-equivalent) variant of Kelley's definition in 1970. Subnets in the sense of Willard and subnets in the sense of Kelley are the most commonly used definitions of "subnet" but they are each not equivalent to the concept of "subordinate filter", which is the analog of "subsequence" for filters (they are not equivalent in the sense that there exist subordinate filters on whose filter/subordinate–filter relationship cannot be described in terms of the corresponding net/subnet relationship). A third definition of "subnet" (not equivalent to those given by Kelley or Willard) that is equivalent to the concept of "subordinate filter" was introduced independently by Smiley (1957), Aarnes and Andenaes (1972), Murdeshwar (1983), and possibly others, although it is not often used. This article discusses the definition due to Stephen Willard (the other definitions are described in the article Filters in topology#Subnets). (en)
gold:hypernym	Generalization
prov:wasDerivedFrom	wikipedia-en:Subnet_(mathematics)?oldid=1121219125&ns=0
page length (characters) of wiki page	14472 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Subnet_(mathematics)
is Link from a Wikipage to another Wikipage of	John L. Kelley Axiomatic foundations of topological spaces Filter (set theory) Filters in topology Accumulation point Cofinal (mathematics) Net (mathematics) Open and closed maps Cofinal subnet
is Wikipage redirect of	Cofinal subnet
is foaf:primaryTopic of	wikipedia-en:Subnet_(mathematics)

Faceted Search & Find service v1.17_git139 as of Feb 29 2024

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 08.03.3330 as of Mar 19 2024, on Linux (x86_64-generic-linux-glibc212), Single-Server Edition (378 GB total memory, 67 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2024 OpenLink Software