In mathematics, specifically in topology,the interior of a subset S of a topological space X is the union of all subsets of S that are open in X. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions.

Property Value
dbo:abstract
• In mathematics, specifically in topology,the interior of a subset S of a topological space X is the union of all subsets of S that are open in X. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions. The exterior of a set S is the complement of the closure of S; it consists of the points that are in neither the set nor its boundary. The interior, boundary, and exterior of a subset together partition the whole space into three blocks (or fewer when one or more of these is empty). The interior and exterior are always open while the boundary is always closed. Sets with empty interior have been called boundary sets. (en)
dbo:thumbnail
dbo:wikiPageID
• 55610 (xsd:integer)
dbo:wikiPageLength
• 9882 (xsd:integer)
dbo:wikiPageRevisionID
• 984235896 (xsd:integer)
dbp:id
• 3123 (xsd:integer)
dbp:mathStatement
• Let be a complete metric space and let be a sequence of subsets of . * If each is closed in then . * If each is open in then . (en)
dbp:name
• Theorem (en)
dbp:note
• C. Ursescu (en)
dbp:title
• Interior (en)
dbp:wikiPageUsesTemplate
dct:subject
rdf:type
rdfs:comment
• In mathematics, specifically in topology,the interior of a subset S of a topological space X is the union of all subsets of S that are open in X. A point that is in the interior of S is an interior point of S. The interior of S is the complement of the closure of the complement of S. In this sense interior and closure are dual notions. (en)
rdfs:label
• Interior (topology) (en)
owl:sameAs
prov:wasDerivedFrom
foaf:depiction
foaf:isPrimaryTopicOf
is dbo:designCompany of
is dbo:designer of
is dbo:wikiPageDisambiguates of
is dbo:wikiPageRedirects of